This was a short story in a SciFi anthology I read in my school library about a decade ago. I think the anthology was a few years old, from the early 00s, but it may have been older. It was a small library, and we only had a few anthologies. I think one was a "Best of 2002" (or some other year), and the other was a collection of stories that were specifically about time travel.
The story was set in the near-future, in the United States. Space travel had advanced somewhat and I remember there being a colony on the moon.
The story focuses around a group of scientists who are the first to discover/invent time travel. The time machine in question is a lot like the time machine in Primer, where they set up a stationary device and, once its running, can then send items or information from the present to the past. IIRC, They were struggling to find a purpose for it, but decided to go out for lunch to celebrate. The protagonist had forgotten his wallet, but then had an idea. He opened the device and, viola!, his wallet was there with a note from his future self.
The team decides to use their device as a sort of parcel delivery device, where you could (for a hefty fee) send information or materials to your past self to keep yourself from making mistakes or avert disasters. One specific example I remember was using it to send extra oxygen tanks back in time on a moon colony to keep everyone from asphyxiating.
If I remember right, their company name was sort of a pun on FedEx. I think the story was written in the first person, by one of the founders of the company, but well after the company was established. Maybe he was near the end of his life and decided to make the founding of the company public knowledge?
If I remember any other details, I'll post them here.