If my mother gives up her Green card, can she re-acquire it thru sister?

Hi, my mother has a Green card, but she wants to give up her Green card for now. But if she does so, can my sister who is a US citizen sponsor my mother for a Green card at a future date? And if so, what are the chances of acceptance and how long will it take?
 
Of course, but the F4 category (sibling) has a wait of almost 13 years (longer for people born in Mexico and the Philippines).
 
Sorry, I did not make myself clear. When I said sister I meant my sister. My mother's daughter. So if my mother gives up her Green card now, she can re-apply through her daughter at a later date? And how long will that take?
Thanks
 
Oops, I misread. Yes, she can get it through her daughter at a later date. There is no wait for visa numbers as it is the Immediate Relative category. If she applies from outside the US, the process takes about a year from her daughter filing the petition to her getting the immigrant visa.
 
Hi, my mother-in-law has green card and she traveled for years coming/going back. Now it's been three years, she did not come back. Is she be able to come later if she wants or what should we do? She never turned the Green Card to the Embassy. My wife is US Citizen.
 
Hi, my mother-in-law has green card and she traveled for years coming/going back. Now it's been three years, she did not come back. Is she be able to come later if she wants or what should we do? She never turned the Green Card to the Embassy. My wife is US Citizen.

She will be deemed to have abandoned her green card (after one year absence), your wife will need to file a new petition for her.
 
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