How to transfer messages on to a PC?

I have an Iphone 6 and I have a message folder that holds over 20k messages that i really want to keep. How can i transfer the messages on my phone to my PC? The person who the messages are from has an Android, is there a way to do it with her phone if it's not possible with mine?

You can use a third party tool to transfer the messages you want to your pc
for storage. I think this kind of 3-rd party tool can be more convenient than iTunes, cuz it allows preview.
You can try mobikin assistant for ios.