Backing up text messages on a Macbook Pro

How do i back up the history of my text message from my iPhone 6 plus to my macbook pro? Ive fired out how to get the current messages to come through but i can't figure out how to transfer over the conversation thread to access conversations from weeks, months of even years ago.

My mom recently passed and her and i had a thread of almost years going I've been storing these messages on my phone, id really like to save them and transfer the tread over to my Mac so i can free up the space on my phone.

I have the iPhone 6 plus and it has 16g so i only have about 1g left and can barley even take one or 2 photos before being told theres no more available space and i must delete large files, which surprise majority go the data being held is that lager attachment file. I enjoy going back through my moms messages to remember her, id hate to lose any of them but i also wish i could use my phone ... please help!