Please report your foreign income for the entire year. Separately (on the text entry tab), explain how income was allocated before and after the green card was issued or before and after the date of your move to the U.S., whichever came first.
Which filing option is best: filing as a U.S. resident for the entire year or part of the year?
Filing as a U.S. resident for the entire year (especially if filed jointly with a spouse) means a lower tax rate and higher deductions.
However, filing for the part of the year (from the date you received your GC onwards) is beneficial if you lumped sum foreign pension or bonus at the beginning of the year that can be excluded from your U.S. income if you file for only part of the year.