Proper method to share and access lemmy links that avoids login problems?

It often happens that a given lemmy link didn't match with my own login from another instance. This causes troubles to comment and participate in the thread. This is what I have learned so far. Is there a better method of doing this? Browser extension suggestions are welcome.

Context:

• Have an account @username on instance lemmy.test and being logged in
• Given a lemmy link lemmy.example.com/post/12345
• Want to comment as @[email protected] on lemmy.example.com/post/12345

Expected behavior:

• Opening links from lemmy.example.com automatically recognizes login from lemmy.test, commenting and voting done without problems

Actual behavior:

• Instance lemmy.example.com expects logins only from its own server, not other federated servers like lemmy.test

Manual fix (for web browsers):

• Check for the "federation link" (the icon with five-colored star, is there a name for this?) from linked URL's page. (If the icon does not exist, check Observations below)
• Open "search" from own instance (lemmy.test > search)
• Enter the "federation link" at search bar.
• First result should be a URL that's compatible with the own instance: e.g. lemmy.test/post/98765

Observations:

• If the link and its OP shares the same instance domain (@[email protected] posting to [email protected]), then the federation link should be the link itself (please confirm if this is actually true).
• If not, then the "federation link" has to be obtained.
• INCLUDE HTTPS before domain, otherwise it won't appear in the search:

https://lemmy.example.com/post/12345 OK
lemmy.example.com/post/12345 NOT OK