You need browser addon for userscripts to work: Tampermonkey (Chrome) or Greasemonkey (Firefox) or Violentmonkey.

Watches every deleted message in every discord-channel you have opened, and saves them to your browser localStorage
(it lasts even after reboot).

Trashcan icon with an arrow in the right upper corner of Discord window opens Deleted messages list. It contains a list of deleted messages of active channel
To resize that window move your cursor to the right bottom corner of it.

To record several channels, just open a new browser tab with needed channel and make sure this script is working.
You can switch between channels and every channel will show its deleted messages storage.
You can delete every message from memory by clicking [X] button.
Make sure you enabled auto-update in your userscript settings, so you can get later versions.

Discussion:
Discord: https://discord.gg/BJTk6get7H
Telegram: https://t.me/toolz_maker