Does document.cookie show these cookies if you paste this command in the command line in the Web Console (Firefox/Tools > Web Developer)?

You can enable the Storage tab in the Web Console by clicking the toolbar settings (gear) icon and use the storage inspector to check what cookies are created.

• https://developer.mozilla.org/Tools/Tools_Toolbox#Settings

You can check in the Web Console if there are (JavaScript) error messages about this issue.

You can remove all data stored in Firefox from a specific domain via "Forget About This Site" in the right-click context menu of an history entry ("History > Show All History" or "View > Sidebar > History") or via the about:permissions page.

Using "Forget About This Site" will remove all data stored in Firefox from that domain like bookmarks, cookies, passwords, cache, history, and exceptions, so be cautious and if you have a password or other data from that domain that you do not want to lose then make sure to backup this data or make a note.

You can't recover from this 'forget' unless you have a backup of the involved files.

It doesn't have any lasting effect, so if you revisit such a 'forgotten' website then data from that website will be saved once again.

Before writing the question I checked all those possible things. I found, that a cookie appears for the domain, but with different name, that is why it is not found, because the name has changed. What causes the name change, is a mystery?

I found why it happens.

A command that gives expiry time for cookie is shifted 10 days ahead by FF! If I create a cookie which has to expire in 11 days, than FF shows that it has to expire TOMORROW! Anything less than 10 days create cookies which are already expired that is why they never are seen in cookie-manager.