Going back to old H1 - impact on Stamping?

[kataria]

Will appreciate your advice on this -

A friend started working as a contractor with Company A1, through employer Company A. Company A filed an H1 which is valid until March 2013.

They later switched to a full-time employer Company B and have a valid H1 until August 2013 with Company B. They also have a H1 stamp and have entered the country with an I-94 from Company B.

They are now joining Company A1 on similar contract role as before, through the same employer Company A. The Company A H1 is still valid so I know they can do this.

My Questions -

1. Do they have to file any paperwork through Company A to obtain a valid I-94 under the Company A H1.

2. The H1 stamp is valid until 2013. Next time they enter the US, will they need a new stamp under Company A, or can they enter with the current stamp but with Company A I-797.

Thanks for your help.