Thanks for your question. I will try to help.
Unfortunately, no visitor on a visit visa can apply to extend their stay from within the UK. This is because all visit visas are subject to the condition that the visitor must leave the UK before the expiry of the visa. This is taken to mean that they cannot switch in to another visa category from with the UK.
This is applied very strictly and the application would certainly be rejected.
You will have to make his application (I assume for a spouse visa) from outside the UK after her has returned following his visit here unfortunately.
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