If by texts you mean SMS then yes, there is a way to save them. A couple of ways. actually. The way I use is to create a backup of my phone. It saves the files into a .ipd file. Then I downloaded ABC Amber Blackberry COnverter (free trial) and I open the ipd with it. Once you do that, you can save all your messages to a file, either as one document or as separate docs. I actually bought the program because I liked it so much. Link is here:
Free download ABC Amber BlackBerry Convertor, parse, convert, backup and archive IPD files to CHM, PDF, HTML, Word, Access, Excel, CSV, IPD Extractor
Other people have commented on Dexrex...a website when you can save your info.
https://www.dexrex.com/
I have never used this but some people swear by it. And it's free. There also may be other alternatives.