Is it okay for a customer to send me less than the amount I invoiced because of their wire charges? For example, I invoice $380 and they send me $365. I understand I may have additional charges from my bank, but the $365 is before those are applied.
If you invoice for $380, you should receive $380... then if your payment processor has fees, they are deducted from the $380.
In no instance is it "okay" for a client to send less than the invoiced amount, for whatever reason. If the client must pay fees, then those fees are their problem they should be paid above and beyond any invoice amount. If it costs the client $15 to send you $380, then the client needs to pay $395 to ensure you receive the $380 which was invoiced. All invoices indicate the amount you are to receive, not merely the amount a client should send.
It is not acceptable for any client deduct or factor in any processing fees for the client from your invoice. As your example stands, the client has made you responsible for double processing fees. That would not be acceptable to me. And I'd demand the client send the remaining $15.