How do I approach my compulsive liar

Hi - I'm new here.

I've been with my husband for 10 years, married for 3. It took a few years before I suspected he was lying to me about his age and family history. By that time we had two children so it was harder to get out. Not only that, but aside from the lying, he is a very good husband and father who treats us well and supports us.

I also never had anything concrete to go on other than my suspicions. The more years we were together , the more strange I found it that I'd never met, nor seen any evidence of these family members he had told me about.

Before I married him I gave it serious thought and decided that whilst I didn't believe his story - I knew him as a person and that was more important. I thought there must be some dark secret in his past and when he's ready and trusts me enough to cope with it appropriately he will tell me one day.

A few months ago, just before our fourth child was born, I spoke to him about it. Told him I'd never really believed him since we'd met. Told him I had extensively searched for the people he'd told me about and come up with nothing despite the fact that resources are excellent these days. He had no response to specific things I asked him like 'If your Grandad is really that old then why is he not on the list of the world's 100 oldest people on wiki?' 'If your brother is really in prison in Texas why is he not on the full list of prisoners for Texas available online?' He kind of fell silent then said 'Why would I tell you that if it wasn't true?' Then diverted the conversation by telling me some deep, dark story from his past that slightly explained why he may have been a bit shady and 'lying low' for some years. This killed the conversation for the night, I decided we'd discuss it again - then I had a baby.

A couple of days ago I found evidence that either he HAS lied about his age OR he's using somebody else's identity.

I'm in the process of instructing a private investigator to do a background check on him to include information about his relatives.

I started some research about lying and everything I read about compulsive lying rings true to him.

How do I approach him again? Is he just going to continue lying? What the hell do I do with this now after 10 years and 4 kids?!