One of the earliest myths in the birther belief system is the claim that Barack Obama is really "Barry Soetoro", who lost his US citizenship upon adoption by Lolo Soetoro, an Indonesian national.
This dates back to Philip Berg's original lawsuit, when he claimed that both Barack Obama AND his mother lost their US citizenship upon her marriage, saying in his original complaint (¶ 31) that:
"Obama's mother expatriated her U.S. Citizenship when she married Lolo Soetoro, a citizen of Indonesia and relocated her and her son (Obama) to Indonesia."
Berg cites the Nationality Act of 1940, Section 317(b). But let's see what that says:
"From and after the effective date of this Act, a woman, who was a citizen of the United States at birth, and who has or is believed to have lost her United States citizenship solely by reason of her marriage prior to September 22, 1922, to an alien, and whose marital status with such alien has or shall have terminated, if no other nationality was acquired by affirmative act other than such marriage,shall, from and after the taking of the oath of allegiance prescribed by subsection (b) of section 335 of this Act, be deemed to be a citizen of the United States to the same extent as though her marriage to said alien had taken place on or after September 22, 1922."
This section only applies towards marriages before 22 September 1922. Yet Stanley Ann Dunham married Lolo Soetoro in 1967. This section simply doesn't apply.
But what about the claim that Barack Obama lost his US citizenship. Again we can look to the very same act that Berg cited, the Nationality Act of 1940, Section 401:
"A person who is a national of the United States, whether by birth or naturalization, shall lose his nationality by: (a) Obtaining naturalization in a foreign state, either upon his own application or through the naturalization of a parent having legal custody of such person: Provided, however, That nationality not be lost as the result of the naturalization of a parent unless and until the child shall have attained the age of twenty-three years without acquiring permanent residence in the United States:....."
This section shows that even had Stanley Ann Dunham renounced her US citizenship, it wouldn't have effected Barack Obama's citizenship.
But could Stanley Ann Dunham or Lolo Soetoro renounced Barack Obama's citizenship? Again, the Nationality Act of 1940, Section 407:
"A person having American nationality, who is a minor and is residing in a foreign state with or under the legal custody of a parent who loses American nationality under section 404 of this Act, shall at the same time lose his American nationality if such minor has or acquires the nationality of such foreign state: Provided, That, in such case, American nationality shall not be lost as the result of loss of American nationality by the parent unless and until the child attains the age of twenty-three years without having acquired permanent residence in the United States."
So again we see that nothing that Stanley Ann Dunham or Lolo Soetoro could have done would have affected Barack Obama's US citizenship.
But what Berg doesn't cover in his filings, and is usually ignored by the birthers, is that the 1940 law was amended in 1952 by the 1952 Immigration and Nationality Act, Title III, Chapter 3. And that makes the citizenship status of Barack Obama even clearer. For example, we see section 349 (a), which says that:
"From and after the effective date of this Act a person who is a national of the United States whether by birth or naturalization, shall lose his nationality by --
(1) obtaining naturalization in a foreign state upon his own application, upon an application filed in his behalf by a parent, or duly authorized agent, or through the naturalization of a parent having legal custody of such person: Provided, That nationality shall not be lost by any person under this section as the result of the naturalization of a parent or parents while such person is under the age of twenty-one years, or as the result of naturalization obtained on behalf of a person under twenty-one years of age by a parent, guardian, or duly authorized agent, unless such person shall fail to enter the United States to establish a permanent residence prior to his twenty-fifth birthday: ...."
As you can see here, anything Stanley Ann Dunham or Lolo Soetoro could have done to renounce Barack Obama's US citizenship simply would not have worked in the eyes of US law. Barack Obama himself would have had to do so after his 21st birthday, or after his 25th had he not returned to the United States by then and established a permanent residence.
And when did he return to the United States? In 1971, around his tenth birthday.
Furthermore, the 1952 Immigration and Nationality Act, Title III, Chapter 3, Section 355, says:
"A person having United States nationality, who is under the age of twenty-one and whose residence is in a foreign state with or under the legal custody of a parent who hereafter loses United States nationality under section 350 or 352 of this title, shall also lose his United States nationality if such person has or acquires the nationality of such foreign state: Provided, That, in such case, United States nationality shall not be lost as the result of loss of United States nationality by the parent unless and until the person attains the age of twenty-five years without having established his residence in the United States."
So has we see here, there is no way under US law that Barack Obama could have lost his US citizenship due to action of his own OR that of his mother before he was 21 years of age. Under US law, he maintained his birthright US citizenship with no loss or interruption, and no deed for "naturalization" or any "oaths of citizenship" because Natural-Born US citizens don't require such.
So that's on the US side. What about the Indonesian side of the claim?
Berg has it partly right in that Indonesia didn't allow for dual-citizenship at the time. However, Indonesian citizenship law at the time states the ways that someone could become naturalized in that country and what they would have to do to lose said citizenship.
The law in question is Law No. 62 of 1958, Law on the Citizenship of the Republic of Indonesia, 62/1958 for short. Assuming an adoption took place, it would fall under Article 2 of this law.
"Article 2.
(1)A foreign child of less than 5 years age who is adopted by a citizen of the Republic of Indonesia acquires the citizenship of the Republic of Indonesia, if such an adoption is declared legal by the Pengadilan Negeri at the residence of the person adopting the child."
Note the age limit there - less than 5 years of age. Lolo Soetoro married Stanley Ann Dunham in either 1966 or 1967. This would have made Obama either five or six - over the age limit according to Indonesian law. Furthermore, they didn't move to Indonesia until 1967, when Obama was six years old.
Therefore, under Indonesian law, there was no way via adoption that Indonesian citizenship could have been granted to Barack Obama.
I'd like to note at this time that there is no credible evidence to suppport an adoption claim in the first place. The main records that are used to cite such are Obama's Indonesian School record and the Soetoro-Dunham Hawaiian divorce decree. Neither though say adoption anywhere in the paperwork.
Ironically enough, the Indonesian School record gives Obama's birthplace as "Honolulu, USA". Placing many birthers into claiming that the school record is a credible document to "prove" adoption, but ignoring that by that logic, it's also a credible document to prove birthplace as well.
Also, according to Article 14 of 62/1958:
"(1)If the children as mentioned in article 2 and article 13 reach the age of 21, they loose the citizenship of the Republic of Indonesia again, if and when they make a statement as to that effect. Said statement shall be made within 1 year after the children have reached the age of 21 to the Pengadilan Negeri of Representation of the Republic of Indonesia at their residence."
and Article 17 of 62/1958:
"e.being declared as lost by the Minister of Justice with the approval of the Cabinet Council on the request of the person concerned if the person has reached the age of 21, is domiciled abroad and does not become stateless at the declaration of the citizenship of the Republic of Indonesia as being lost;"
"k.other than for state’s service, domiciling abroad during 5 consecutive years by not declaring one’s wish as to continue being a citizen before the period has lapsed and thereafter every two years; such a wish shall be declared to the Representation of the Republic of Indonesia at one’s residence."
As we can see from all those, even IF Obama had been granted Indonesian citizenship, (which under Indonesian law he couldn't due to being over age and unable to renounce the US citizenship), Obama would have lost the Indonesian citizenship after living outside of the country for five years.
So to recap:
Under US law as shown in Sections 317(b), 401, and 407 of the Nationality Act of 1940, and Sections 349 (a) and 355 of the 1952 Immigration and Nationality Act, Title III, Chapter 3, neither Stanley Ann Dunham or Barack Obama would have lost US citizenship upon marriage to Lolo Soetoro. Neither could Barack Obama have lost US citizenship due to actions taken by his mother.
Under Indonesian Law 62/1958, Article 2, there was no way to grant Indonesian citizenship to Barack Obama due to being over the age limit as defined by Indonesian law. In addition, the inability to renounce Barack Obama's US citizenship would have rendered him unable to be granted Indonesian citizenship until the age of 21, and he would have had to returned to Indonesia to live AFTER his mother divorced Lolo Soetoro to meet the guidelines in Article 5 of that law.
In short, there is no possible way under either United States OR Indonesian law that Barack Obama could have lost his US citizenship and been granted Indonesian citizenship as a child.
This myth is busted.

