Only way I know is to do print screens. SMS messages aren't stored in a location from which downloads are possible.
Update based on @Nighthawk reply: on an iPhone you can also mark the messages in a string, and email them to an email not associated with your Apple ID (or Messages ID). You lose continuity, as the senders names are not included, but the text is present; each SMS on one line. You can edit the email's content once received to make the information look organized. Thanks, Nighthawk, I learned something new today.
Does your daughter have an iPhone? I know of an app for Mac OS that will let you download and print them all quite easily.