Sync won't handle 350 Synced Tabs. I am not sure what the actual limit is, but other users have mentioned that they couldn't Sync 70 Tabs.

Try using Bookmark All Tabs from the tab-strip contextual menu to save the tabs (in a new folder in Bookmarks) in each window that you may have open; each window will save to a separate new folder.

Once those new bookmarks get synced to the new computer you can middle-click (or use Open All in Tabs from the bookmarks contextual menu) to have all the bookmarks in that folder open in Tabs.

Thank you, that worked perfectly!

Note that you can copy the sessionstore.js from one computer to another computer or profile to transefer personal data.

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

• bookmarks and history: places.sqlite
• bookmark backups: JSON backups in the bookmarkbackups folder
• SQLite files like cookies.sqlite (cookies) and formhistory.sqlite (saved form data)
• logins.json and key3.db (decryption key) for Passwords saved in the Password Manager
• cert8.db and possibly cert_override.txt for (intermediate) certificates stored in the Certificate Manager
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other Site Preferences
• sessionstore.js for open tabs and pinned tabs and tab groups

See also:

• https://support.mozilla.org/kb/Recovering+important+data+from+an+old+profile
• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox