Check all documents

You mentioned the gap between OPT and H1B. Did he get the receipt from USCIS before his OPT expired ? Maybe this is the problem.

Check the following Dates:
1) OPT expiration date
2) Dated receipt from USCIS for the first H1B petition, and the date he received this.
3) Date of the first I797 approved,a dn the date he received it.
4) Dated receipt from USCIS for the second H1B transfer petition, and the date he received this.
5) Date of the second I797 approved,and the date he received it.

Now, check to see if there is really any gap from 1 to 5. Because if you miss any one, it looks lika a gap.
Good Luck.