ask for offer in writing, explain why, and that you'd prefer A, see if they are open to matching B's offer. If so, you might want to take their initial offer to B.

Get B's offer in writing and go to A. Tell A if they match it, you'll work for them.

Do so, that is, if they match B's offer, work for A. Explain to B, but invite them to contact you sometime in the future to see if you are happy at A. Use B's contact to either move to B if A isn't great or to negotiate from position from strength at A.

But work at A to start with.