B1 and H1b

I currently have B1 which is valid till 2020. This year I got my H1b I129 approved and currently have I797. I need to travel to US on a business trip for a month. I will go for H1b stamping after I come back to India later travel to US after couple of months on H1b. In this situation will I face any issue at port of entry for business trip as I have I797 with me. Which is the best way for me to go for business trip now and later go on long term. I mean get the H1b stamping done before I go on business trip or get it done after I come back.
Note: the company which is processing my H1b is different from the company through which I am going on business trip.
Please suggest the best way so that I do not face any issues at port of entry during my both the visits.
Thanks in advance.