The files created with Tedit can be found there : ~phablet/.local/share/tedit.fulvio/
You can access it with the file manager and move or copy them wherever you want.
I am doing the same, but mostly from the terminal (copying to/from USB). I took the liberty to create myself a short-cut (~phablet: ln -s /.local/share/tedit.fulvio/ MyTextFiles)
The file manager (in unlocked mode) displays the symlink "MyTextFiles" as if it was a directory, so you don't have to navigate the full path every time.
But if (as your title suggest) you want the other way around, I'm not sure if Tedit can handle it... but I didn't read the code, so maybe.
I have copied many a text file to tedit's directory. From there, it can open them alright (settings icon / open / select a file by touching it / swipe to the left, click the "edit" icon).
I'm very glad about tedit, it has proven to be really helpful to me. It stores plain text that I can re-use later any time, anywhere. I tried the Note app first, but it's actually storing XML (~phablet/.local/share/com.ubuntu.reminders/); fine for what it is, but not what I need.
BTW, I got really skilled at using vi with the on-screen keyboard, I don't need any other games.
(explanation: I'm using "view" aka "vi -R" when I want to read a config file, since "less" seems to mess up the terminal, and "cat" isn't always an option. Maybe I could start using uText for that like @Giiba mentioned. Since the root file system is read-only, no risk messing up.)