B1/B2 to H1B status change

Hello Sir,

I have a valid B1/B2 visa and I have travelled to US multiple times. I also have H1B approval and I am eligible for drop box. My employer is telling that if I don't get H1B stamped via dropbox I can travel on B1 and then change the status to H1. Are there any issues at immigration if I come on B1/B2?

Regards,
Santosh
 
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