A Person Using PayPal using A Fake Address

[WOO2]

Hello,
I am dealing with a customer who used PayPal to pay for an item he bought on eBay from me. He gives a fake address on PayPal, then asked me to send to a different address. Now he has not received his item. He leaves nothing but negative feedback for sellers stating he did not receive his items.
Yes, I made the mistake of sending to a different address to his PayPal address, but eBay said as they can see he asked me to post to another address through eBay, they have my back.
The problem I have is that a claim is likely come, he is potentially stealing many items and is able to use PayPal with a fraudulent address. Now although the item price is only £15, I cannot allow this to happen time and time again. If eBay took action it would be great, until he uses another profile, name or address and carries on. But how does a scammer get away with theft through a fraudulent address on PayPal?
Are there any checks? The postcode he gives does not exist!
I am a bit stressed as I have to keep dealing with people like this and PayPal don't have a single feature I can find to report him through. I would also like to report him to the police, as he might be stealing hundreds, or thousands of pounds from people. He may even be giving a fake name or using a stolen card to have a PayPal account? If you are a thief and use fake addresses, anything is possible! I am angry that people can get away with anything like this.
Please can someone advise me on how to report this member to PayPal? Because eBay often allow people like him to carry on, but an institution like PayPal allowing a fake address to be used to hold an account must be illegal?
Thank you in advance for your help.

[WOO2]

To add to the above details, the street name does not exist either. He said it was his old address, now I know he will say it is a mistake if I pull him up on it, but he has likely gained much from his 'mistake!'

I need to allow this to play out, allow him to claim, negative, then have eBay step in.
But this cannot be allowed to happen on PayPal, imagine banks allowing people to open accounts in fake names or addresses, then stealing or money laundering. I Googled his name and business name and the name he has given ties up to a 'business account'. I want people like him to be addressed by the law! I am not going to let this one slide as I am finding more and more people to be dishonest and use many accounts and bogus addresses to gain free items.
As you can imagine, we are all paying for this mass theft.