I'm using a similar approach, just instead chat/forward messages to a special private group (I think 'Saved' didn't exist when I set this up).
Then I've got a script (https://github.com/karlicoss/telegram2org) that checks for new messages in this group every hour or so (cron) and appends Org-mode formatted messages to a special file.
There are some extra features, like automatically mapping select senders into org-mode tags (yes, I do keep tags for closest friends :D ).
That makes it always show up when I search something (adressing the problem of finding information), I also can easily transform it into a proper todo/task if necessary.
