Thanks for your patience.
Basically, he has made the wrong applicaiton and disadvantaged himself because of it.
The process for any person on a visa is that must first obtain "indefinite leave to remain" by applying for it. Once they have obtained ILR they can then apply for naturalisation because they are no longer time-limited.
He would probably have been eligible to apply for ILR before his current visa expired. However, because his visa has now expired he, technically, no longer has leave to remain in the UK. The fact that he no longer has leave to remain in the UK is a general ground on which the UKBA can refuse an application that he submits now.
Although, it's very kind of you to offer, it's not really a solution for them for you to sponsor him because his immigration status would be linked to his employment with you. Instead, he needs to make an application based on his married.
The question is whether he should now apply for ILR or simply apply for further leave to remain, which is an extension by another name.
In both cases he would have to argue that they should disregard the lack of leave to remain and allow the application. Additionall, the would have to argue that it would be disproportionate and unreasonable of them to expect him to return to his home country only to make an application form there which would be accepted a matter of weeks/months later.
My view is that he should apply for ILR because although it's quite probable that they would not give him it, it is highly possible that they would give him further leave to remain anyway and extend his visa because of the circumstances.
It's going to be a bit of a fight and he would have to instruct a UK based solicitor in order to prepare the application quickly and submit his statements in support explaining his honest mistake and misunderstanding of the immigration rules which led to him prematurely thinking that he could apply for naturalisation now.
It might take a bit of time to sort out as well, so they should mentally prepare themselves for the process to be fairly demanding.
Additionally, time is of the essence and they need to see a solicitor as soon as possible to get cracking.