Boost Mobile does not offer an option to view text messages from an online phone account, as of 2014. However, there are still several options available for backing up texts online, including using the Boost Mobile mail service and installing a designated app to record text messages.Know More
To back up text messages to an email account, begin by syncing the desired email account with the Boost Mobile phone. Then, go to the Messages screen on the phone, and choose "Back up SMS," followed by "Back up SMS via mail," from the menu.
Another option to view Boost Mobile text messages from an online account is to install a text-tracking app, such as mSpy, on the phone. These apps log text messages and allow them to be read online later.