I don't trust the source, he/she wants me to contact them outside of ebay mailing.

Go with your instincts as that's a classic way that scammers operate.

I've just contacted them through ebay question, and invoiced them

They'll either pay with a stolen credit card or Paypal account or they send a false Email telling you that payment has been made,(there are also other deceptions they use).

Don't send them anything.

Contact eBay and use Selling and Managing Your Item

http://pages.ebay.com.au/help/contact_us/_base/index_selection.html

Thanks,PJ, :-x (I knew that link was around somewhere),:-D