Don't sponsor him until you become a U.S. citizen. Then, he can get his green card without leaving the U.S. Most probably, his shoplifting conviction constitutes "one petty offense" meaning that there will be no negative immigration consequences.
(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
No problem. You could file a petition on his behalf now (as an lpr). That petition will become an "immnediate relative petition" once you obtain your US citizenship. Once the petition is upgraded he will be able to adjust his status to that of a legal permanent resident. He may need a waiver for his criminal case but should not have any problems as long as he is otherwise admissible. I suggest that you get the help of an EXPERIENCED immigration attorney.
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Law Office of Luis A. Guerra (954) 434-5800. This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice.