In determining the U.S. tax basis of assets acquired by a foreign citizen, historical cost is used (as in the case of a U.S. citizen). If the historical cost is denominated in a foreign currency, the equivalent U.S. dollar amount is determined by using the foreign exchange rate at the time the asset was purchased.
In general, the taxpayer’s cost basis for purchased property has been determined to be the initial expenditure in the foreign jurisdiction
Generally, all of the same US tax rules apply to outside the country real estate that apply to inside the U.S. properties
Property located outside the country, you're required to depreciate the cost over 40 years.
For U.S. tax purpose the date you become eligible to file a U.S. [rental placed in service]
First Year of Residency
If you are a U.S. resident for the calendar year, but you were not a U.S. resident at any time during the preceding calendar year, you are a U.S. resident only for the part of the calendar year that begins on the residency starting date. You are a nonresident alien for the part of the year before that date.
Once you get a green card, you automatically become a U.S. tax resident and you must declare your entire income to the U.S. government.
Topic 851 - Resident and Nonresident Aliens
https://www.irs.gov/taxtopics/tc851.html
Rental Property Income and Expenses
https://ttlc.intuit.com/replies/3288530
