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2 things to make sure of is that you are logged in on the IPad with the same Apple ID as the IPhone. Also, go to Settings>messages, and make sure imessage is turned on. if you have a WiFi only iPad, it will only sync up when you’re on WiFi. If it has Tmobile service on it, then it will sync up automatically.
as for facebook messenger, make sure you are logged into the correct Facebook account. Those messages on Facebook get saved through Facebook, not your device, so you should always have access to then no matter what device you’re on!
Hope that helped!