[Tutor] How to deploy seamless script updates to your "clients"?

[Juan C.]

I have some Python 3.6.0 scripts that my co-workers use for some small
and medium tasks. Whenever I have time I fix some bugs and add some
features to said scripts to make their lives (and mine :D) easier, but
there's a problem: I need to send a new script via email/chat/whatever
and they have to replace it wherever they use it, such a hassle.

How would I go to put a "update module" inside my script? I was
thinking about using Git, because those scripts are already in
personal repositories so that I can keep track of changes. Will I have
to setup any special permissions so that the scripts can pull requests
from my private repositories?

I was thinking of something like "check for update before start", if
an update is found the script would replace itself with the newer
version and restart, is that possible? For example, 'cool-tool.py'
v0.2 starts and find that version v0.3 is out, so it downloads and
replace 'cool-tool.py' code with newer code and restart as v0.3.