is it mandatory to have a US work experience to work in h1b?

Iam in US in H4 visa from 2013. I have work experience in testing in India. I got my H1b approved this year thru a consultancy. Now my consultancy is asking me to put a fake US experience to present it to clients.Will it affect my future job search and can i search thru monster and dice without putting US experience and mentioning only my India job experience? Please advice

I would never go down the route. It may cause other issues in future.