My Mom is widow, Filipino citizen but stayed here in American Samoa, is she can apply a green card through mail ?

More evidence is needed. She will need evidence to prove the relationship and her deceased husband's U. S. Citizenship. She should file a form I-360, among other documentation within two years of his death. She has additional processing that must commence with the State Department. This is complicated. The situation can get more complicated and delayed due to confusion as to how the system works. Some have lost visa opportunities as a result. I strongly recommend that she hire a competent and experienced U. S. Licensed Immigration and Visa Attorney.

I concur with Mr. Dixler's very comprehensive answer. He said it all. All that is left for me is to agree.

Dixler is 'spot-on"