is H1B restamping needed

HI I recently(Last month) got my H1B stamped from employer A I was working for , but unfortunately that project ramped down and employer A has no current opening in USA. If i join other company B , do I need to go for restamping again ? My current H1B from employer A is valid till DEC 2018 but I didnt travel to USA on this . Please help after reading online I am confused and need to decide before I join B

You can use the employer A visa until its expiry. But you need to have the employer B’s approval notice i-797 with you when you travel. Without I-797 you wont be allowed into USA at the port of entry. You need not go for re-stamping for employer B.

You may be asked questions on your new job at employer B by the immigration officer, on how you got hired, what is the nature of the job etc.