I did that, but it did not transfer everything. Also, some transferred messages had their original dates changed to 1970. That's what I don't understand.
As I remember, Google Messages should automatically sync all of your old messages with itself - though I'm not sure if it will sync with the web client as well.
Could give it some time to finish syncing first, or try clearing Google Messages' app cache to see if that forces a resync.
As for the dates - could be that the two apps are using different date formats and were not able to read the messages metadata properly? I'm honestly not sure - but future messages should sync up with the current time and date.
