You can solicit the help of a freelancer to do your work but you can’t solicit to pay for an answer to a question because that’s not what google groups is for
He could perhaps just offer a bounty? It's perhaps the same thing. It is very common in the open-source community to do that. But, agreed, the problem would need to be very explicit and the solution verifiable and given to the first solver. Perhaps posting a link from the google group to a bounty site would be OK here?
(btw- you might not have seen some of the other google groups... the ethical bar in general is perhaps not what you think it is! ;')