In the UK I think you're probably right, but it's not the clearest situation. You may argue that all of the communication up to the point where he agreed with their offer is part of the contract.
> However, in some circumstances, for example when copyright is not dealt with in the contract to commission the work, courts may be willing to find that there is an implied licence allowing the commissioner to use the work for the purpose for which it was commissioned. This does not necessarily result in a transfer of ownership. Instead, the commissioner of the work may only get a limited non-exclusive licence. This situation demonstrates the importance of establishing who owns copyright through a contract.
It's very likely that an attempt on his part to sue Microsoft would fail on the grounds that a tacit agreement was reached for the use of the work, based on his acceptance of payment. However, it doesn't sound like there was any agreement, tacit or otherwise, that the license should be exclusive. So he's still well within his rights to dedicate it to the public domain.
> However, in some circumstances, for example when copyright is not dealt with in the contract to commission the work, courts may be willing to find that there is an implied licence allowing the commissioner to use the work for the purpose for which it was commissioned. This does not necessarily result in a transfer of ownership. Instead, the commissioner of the work may only get a limited non-exclusive licence. This situation demonstrates the importance of establishing who owns copyright through a contract.
[1]: https://www.gov.uk/guidance/ownership-of-copyright-works