Initiate GC on L1 visa with an approved H1 petition


I have L1A visa with Company A. I got H1B petition approved with Company B and valid from Oct 1st. Now, if Company A wants to initiate GC for me, what will be my options? Will there be any issues? How should this be handled? I would like to stay with Company A, in case they start the GC processing.

Advice pls.



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