With that out of the way, pick a solution from https://www.google.com/search?hl=en&as_q=android+save+sms+to+computer
If you need to know why this is not considered proof, you talk to your lawyer.
Bob
I have some very important text that I would like to document in another sort of way. If there is a way to send the entire stream from one person to a word document that is really what I would love to do. Do you know of anyway to do this?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic