There is mail service to Ecuador. We have a post office box and get mail there, but if you put the recipient’s physical address on the envelope the postal service will usually hand deliver it even if there is no external mailbox. That might be a little risky though with sending money so you might want to try another option. If you want to send a check you’ll need to get an international cashier’s check from your bank and you could send it through DHL or FedEx. Your best option though might be Western Union.
Another idea is to use PayPal. I use this frequently for sending money to people in other countries and there’s no cost. You just need to make sure that the sending and receiving parties both have an account and then choose the option of sending money to friends or family when you make your payment. If you choose the option of paying for goods or services PayPal will keep a percentage of the payment as a fee.