H1B transfer- objections raised by current employer

Couple of questions :1. Can i transfer my H1b from company A to company B ? Any chances of rejection from USICS ? I have not travelled from company A, so can employer raise an objection to stop my transfer to USICS?2. Should I move to company B only after the transfer done ? I am in India now , and i understand that transfer takes 2-3 months and my notice period is 2 months. No company here in India no company will wait for 6 months for onbording. I have got my visa stamped from Company A and have copies of all the documents and originals.Pls suggest the best and efficient way to move from company A to B efficiently and safely.