My text messages are still on the iphone5, even though I removed the sim card. Will I lose the texts when I install a new sim card

My text messages are still on my iphone5, even though I removed the sim card. Will I lose the texts when I install a new sim card?

I want to keep my old text messages. They document old events and conversations with friends.

I now have a new iPhone and want to give this one to my daughter. What happens when she puts a new sim card in?

I'm trying to save the texts via screenshots, but it's taking a long time and she needs to use the phone.

Thanks for any help.