When you invite a supplier you would raise the invite from a supplier record already created in your account. So when you say the suppliers don’t appear, I presume you’re talking about the invoices they’re raising?
I’ll send you a PM to get more information, that’s probably best for now.
EDIT: Just a note here for others… When you connect with your supplier retrospective invoices aren’t brought into the account. Only invoices created after the invitation was accepted will be imported.