Is my girlfriend a US citizen?

Her grandmother was born in the US in Boston. She became a nurse and worked in Boston. She married a doctor and they moved to Argentina. Then my girlfriends mom was born in Argentina. So she would be a US citizen correct?

Then my girlfriend was born in Argentina. Would she be a US citizen then? None of the proper paperwork was filed for her moms birth with the US Consulate when she was born.

Your girlfriends grandmother is a US citizen, her mother isn't, and neither is she since both were born in Argentina.

You need to provide more detailed information to determine whether she and her mother have US citizenship (e.g. when each of them was born, whether they were born in wedlock or out of wedlock, the periods that the US citizen parent spent in the US prior to the birth, whether the other parent was a US citizen, etc.).

Most likely, her mother is a US citizen, but she isn't. In order to pass on US citizenship to a child born outside the US, the US citizen parent(s) need to meet certain requirements specified in the law. Whether "paperwork" was filed is irrelevant; the citizenship is automatic if the conditions in the law are met.

In particular, if the child was born abroad in wedlock to one US citizen parent and one non-US-national parent, the US citizen parent must have been physically present in the US before the child's birth for a cumulative total of 5 years, including 2 years after turning 14 (for a child born after 1986), or a cumulative total of 10 years, including 5 years after turning 14 (for a child born between 1952 and 1986), or a cumulative total of 10 years, including 5 years after turning 16 (for a child born between 1940 and 1952). For a child born out of wedlock to a US citizen mother, the mother had to have been physically present in the US before the child's birth for some continuous period of 1 year.

Her grandmother probably spent more than enough time in the US prior to moving abroad to be able to pass US citizenship onto her mother. However, assuming her mother never spent a significant amount of time in the US, her mother wouldn't have been able to pass on US citizenship onto her.

If she is under 18, there is a way for her to get citizenship without moving to the US. But otherwise, the only way for her to get US citizenship is to first immigrate to the US (become a US permanent resident), either by being petitioned by her mother (which would require her mother live in the US, and also there would be a long wait if she is over 21) or some other means, and then apply for naturalization after a number of years living in the US as a permanent resident.

Great, thank you for the answer. That's just what I was looking for.