I would love Firefox Sync too, but a lot of times it just doesn't send the tab I wanted (I always fallback to checking what is open on my other browser).
You need to re-sync in your PC side then it will show the tabs that you sent. I had issues with FF Sync with not appearing on the other side. It is usually that Firefox haven't start the syncing that you have to tell it to sync now.
If you are using Android, disable the battery optimization on Firefox in Android setting.
If you are using Android, disable the battery optimization on Firefox in Android setting.