Please advice, how to ask for promotion.

Hello,

I understand it's not a good time to ask for promotion under today economic environment. But my situation is a bit different.

I worked as contractor for company A onsite for few years, and my contract company is B. My boss from B company told me that I should get promotion but there is not much he could do because I am underpay by the A, so I should talk to A's managers about getting the promotion which B company will get more contract money to pay me.

So my question is, how do I ask for this promotion? Should I even mention that my boss from B said? Should I talk to A's managers in person, by email or by chat?

Thanks for any advise!