The backup you created with iTunes will be saved as .SQL|TE_DB files and you can't read it directly.  You can use an iTunes data extractor to extract the texts onto computer and save messages as excel files. You can read the messages whenever you want.

To read text
messages from iPhone backup first you need to installed iExplorer. 1.iExplorer can load, read and export text messages that are either on
your phone or ones that have been saved in an iTunes Backup already on your
computer.

2.To access text messages on an iPhone, open iExplorer and connect your
iPhone to your computer. You should see the Device Overview screen appear. From this screen
navigate to Data --> Messages or from the left column, under your device's name, navigate to Backups --> Messages.

3.  After clicking on Messages for either an iPhone backup or a currently
connected iPhone device, iExplorer will load your text message database.