delhiwala,
By employment letter it means that before leaving get a letter from your employer which says that you are a bonafide employee of the country and immigration officials should let you in because the company needs you to come back.
Also about your H-1 question, I think your H-1 is questionable if you left the Company A and Joined Company B and then again joined company A.
Because in a way your H-1 was transferred from Co. A to Co. B now for you to work for company A again it has to be transferred again.
In case you didn't do anything after you left Co. A (or you were on bench) it would be ok to use H-1 because it was never transferred to any other employer.
Also check some other threads everyone says it's better to use H-1 instead of EAD if you don't have 140 approved or until your green card processing is going on because god forbid if something wrong happens with your GC process, your status can fall back on H-1. If you are working on EAD, you are immediately out of status.
Check with another lawyer(specialist). Also try to see if you can get on to Murthy Chat with attorney murthy, you might get an exact answer from there.