This is a very unusual situaiton.
I note in your final reply you state "..he may have been approved..". I don't know what you are basing this on, but you have to find out for sure what his current status is in this country.
If he was married in the first place to a UK citizen then he should have applied for a spouses visa under his true name.
Ideally, he would marry you and then apply for a spouses visa. The UKBA would usually require him to make the application from his home country because of his overstay. The overstay in and of itself would not be grounds for refusal. If there were exceptional circumstances (eg that he is required to care for the child) though he could argue that he should be allowed to make his application from here. There would be only a very small chance that he would be successful and he would have to prove that these exceptional circumstances.
The issue of his passport needs to be resolved. He needs this (or a replacement) if he is to make an application to stay here. If he can get someone to send his passport to him from Pakistan then he should do this. Once he has his passport you should see an immigration solicitor and explain your situation to them. They may advise after seeing the specifics of his case and taking your instructions that he should apply for discretionary leave to remain on the basis that he has a child in the UK with you (a UK national) and needs leave to remain to provide care to the child. He would obviously have to come clean about his previous fraudulent application.
The difficulty is that he has attempted to secure asylum by deception using a fake passport. This is very serious and the UKBA reserve the right to curtail any leave to remain granted as a result of deception.
My advice would be to contact the UKBA in writing to establish whether or not he has been granted asylum. At the same time see if he can obtain his real passport from Pakistan. Once you have established this he should then take all his documentation to a local immigration solicitor asking for a fixed fee consultation about his possible application for leave to remain
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