Hi Khanya,
I appreciate the stress involved in your current situation and I fear you may be one of many who find themselves in a tough spot right now.
As you are in negative equity you don't have the option of refinancing to a different lender, so the only option is for your ex-partner to take over the mortgage with the current lender.
As for what types of income the lender will deem acceptable, that will depend on the lender. Some are happy to accept a lodger whilst others will ignore it.
The best advice is for your ex to seek independent financial advice from a
mortgage broker. I appreciate you say he has already done this via a friend but I got the impression you didn't feel that this was neceassarily the best advice available.
If you can say who the lender is and give me some details about your partners income, lenghth of time self employed, net profit for last few years, total loan outstanding, and also any other debts he has, then I may be able to offer some advice.
Dan