Hi Hugo,
Here is some info on Debian based systems runlevels and init scripts:
https://www.debian-administration.org/articles/28
https://wiki.debian.org/RunLevel
Here are the steps you need to follow:
1. Add the script to the /etc/init.d/ directory.
2. Make it executable.
3. Update the runtime control with the following command:
sudo update-rc.d <script_name> defaults
This will add the needed symbolic links to the /etc/rc#.d/ (runtime control) directories.
4. Remove it with:
sudo update-rc.d -f <script_name> remove
Best regards,
Miroslav