Translation of supuesto

His name was Leo and he would become a good friend of mine during the next two weeks. He had a lovely girlfriend where he stayed during my visit. Basically, I slept in his place when he was away.
On Friday, I can send it from the US. But I would send it from here with EMS or even better with UPS, including delivery confirmation and tracking. From the US there will be no return address or tracking.
The travel agent's representative promised that they would return us the difference of the money. They also assured us that we would get special treatment, such as extra drinks and a Kayak expedition.