That's a great question, it's always good to if you're able to access your backed up files from another device. Yes, it is possible. If your text messages have been backed up to your iCould account, you'll be able to view your messages on almost any Apple device, once signed in with your own Apple ID. - BrittanyR_VZW
Is it possible to read text messages on another phone on my account with my i phone
Yes, using Integrated Messaging. Just log in to Message+ using the phone number/profile of the phone/line on your account whose messages you want to see/monitor.