That all depends. Is he a good employee? I mean... he came to you and talked to you about it, so it's not like he was trying to hide it.
Sounds like you already lost this customers business due to the flatbed they bought. If they don't hire this guy, they'll probably hire someone else... so either way, youre not gaining / losing anything either way.
If I were in the situation (I'm not an owner...) If a company wanted me to work weekends with them, I would.. but NOT if they were a previous customer of the company I currently work at. I probably wouldn't even mention it to my boss, because it's not his concern what I do on off hours...
The tricky part here, is that this place was your customer before. Now I get where your coming from with saying no. But if your employee is struggling, and it's a one time thing... why not let him make ends meet? Or meet him halfway.... give him a little raise so he doesn't NEED to work 2 jobs. even $1 an hour is enough to buy a used car / maintain it. If you appreciate your employee (Based on what I know, he seems like a good one, letting you know about the situation), then it's worth it to keep him around.
I see what my company charges for most of the vinyl installs, and stuff I print. And I think to myself how I can do it for half the price, and make a killing. I'm sure I could steal some customers, as most of them know me by my installations... but I never would. I actually thought about buying a wide format printer, and getting into car wraps. Use what I know from this company, and start my own side business which doesn't compete with them. Maybe offer that to your employee.
But it sounds like this customer was your employees customer before he started working for you. They probably have a good relationship / want to work with eachother. Weight in the benefits of keeping your employee happy, and losing the customers bussiness, which it sounds like you already lost most of it. Heck, maybe the customer decides to offer him a fulltime job for more money, then what?
Remember...employees arent your personal property to boss around. They're humans too - If it's not too big of a deal for you, let it be. If it's something you find unacceptable, then let him know. He's not doing anything wrong, just let him know if he works there, your not comfortable with him still working for you, and it'd be no hard feelings.