回复：Hi, Pijiang, Can I apply the immigration for

   I am a US citizen since 2003. In last several years, I tried to invite my mother (she is 80 years now) to visite me for many times. She always be rejected for visa in Shanghai. I ask my daughter to invite her again, but was rejected again in yesterday.

 So, can I apply the  immigration for her?

-Yes.

 Since she is 80 now, will she be approven?

-Yes.

   Also, How long it will take? 

-Normally 6 months to one year.

( I could not find this info in Visa Bulletin, since only visa date  for kids or brother/sister is there)

-your mother GC application has no 排期 under your sponsor (or say "排期 is always current).