You can create a "backup" file or an "export" file to transfer the bookmarks. Unfortunately, this doesn't transfer the little site icons. Those will get picked up as the bookmarks are used.

The trick is that each user has their own Desktop and Documents folders, so where can you save the file for sharing between users?

Windows 10 might have a handy way to do that but, if not, you could create a new folder on the C drive, such as

C:\OurStuff

and put the backup/export files in there.

Here are the steps to create those files from your Firefox. While you only need one to work, you might as well create both just in case:

• Restore bookmarks from backup or move them to another computer
• Export Firefox bookmarks to an HTML file to back up or transfer bookmarks

Then here are the steps to bring them into the new Firefox (again, if the first method works, ignore the second method):

• Restore bookmarks from backup or move them to another computer
• Import Bookmarks from an HTML file

Success?

If you start Windows File Explorer as administrator then you should be able to copy files from one Windows account to another Windows account. Otherwise you can first copy the files to an intermediate location that both accounts can access.

You can copy files like these with Firefox closed to the current profile folder to recover specific data.

• bookmarks and history: places.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (passwords) and key4.db (58+) or key3.db (57 and older) (decryption key) for Passwords saved in the Password Manager
  if you only have key3.db then make sure to remove an existing key4.db
• cert9.db (58+) or cert8.db (57 and older) for (intermediate) certificates stored in the Certificate Manager
  if you only have cert8.db then make sure to remove an existing cert9.db
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)