There is no such thing called "h1b transfer" unless you have already filed I-485 & pending, in your case its obivious you havent !! Good luck !!!

 If you just got your h1 from company A, I think you need to wait for 3 months before you can transfer your h1 to company B. 
I am not 100 % sure though. But I think you can have mulitple h1s . You can ask your company B to file your h1.

 @soul_survivor  You can transfer your h1b from company A to company B. 
http://www.xielaw.com/immigration-faqs/h1b-faqs/h-1b-transfer-faqs.html

 @sojho keto  Better contact some immigration lawyer.

 @soul survivor,
To understand more precisely and accurately the term h1b transfer is used instead of the term  filing new h1b with new company.
Thanks.

@atiranjeet.
such a weird answer dude. but thank anyways. how could i wait for 3 months with company 'A' . As per my understanding, you must have job when you are on h1b. If you wait that much time you are out of status.

@prankster
thank you for the information

Do any one of you know a good immigration lawyer.  Sasto and Bharpardo!!