Can we travel to US on H4 when H1 is underway?

My husband is currently in India and we have filed his H1 for 2013 quota. He has a valid H4 visa. Is it ok to travel on H4 even after the H1 petition is approved or is it safe to be in US before H1 gets approved

Please respond ! Thanks

Also please let me know if 2 companies can apply for H1b for the same person

I think its OK to travel on stamped H4 VISA while his H1B petition is still under process.

Only thing is that if the petition was filed w/ COS, USCIS might reject the COS application and consider only his H1B petition if he travelled to India after filing the petition.

Yes, 2 different companies can apply H1B for same person.

He can travel to US on H-4 w/o impacting his H-1 processing. Once the H-1 gets approved, he can apply for COS from H-4 to H-1 and can then start working on H-1 from COS approval date. The other option is to leave US, get H-1 visa stamped and enter US on stamped H-1 visa.

Leaving US and getting the Visa stamped is a big risk which we are not ready to take. Since my husband didn’t do his MS here, chances of getting rejected is more prevalent. Also do you know how much it costs for a COS and how long it takes to get the approval?

COS would cost $325.00 and it may take 2-3 months for it to get processed.