To transfer android phone text messages to computer, you can try Coolmuster Android Backup Assistant, it's easy to use, have a try.
I have using AirDroid for file transfer for a while and love about it. The messages on my phone(Galaxy S6 Edge) almost reaches the limits. so i need to back up them on my computer, then i can delete the old ones. However, i didn't find such a function on AirDroid, am i wrong? Is there anyway to get that? It's urgent, please help if you knew about it. thanksIf you can't do that with AirDroid, you can search some android backup tools on google. how to save text messages on galaxy