I like this story. It has good flow throughout and the prose is crisp and enjoyable. The pacing was good; there weren't any passages that dragged or felt rushed.
I was thrown off a bit by the "landlord" being a woman.
I thought it odd that the protagonist knew exactly down to the second how long transferring the data from the phone took. Wouldn't that depend on the amount of data, its format, etc. ? Considering how bad every single file system known to me is about estimating how long a certain data transfer will take, this seems quite implausible to me. To make it more plausible, you could maybe give us the progress as a percentage along with the rough estimate of how long it'll take based on trials with the dummy phone.
I'm with Mandamon in that the first line is excellent.
I also especially liked the paragraph about not knowing your mark on page three.
There are a lot of powerful lines in this story. This is one I liked especially:
Straightforward, but very moving. I would only suggest a tiny alteration: to remove the "But." Without it, I think the message is even clearer and the impact is increased by the parallelism of with the previous sentence.
I think the ending wasn't quite as good as the rest of the story. It was a satisfying ending, but it lacked the sort of punch I had hoped for.
Still, this is an excellent story and I enjoyed reading it.