Can Huawei n7 back up short messages?

You can back it up. Download a mobile phone backup software casually.

My mobile phone backups are all done through the application treasure.

After connecting the mobile phone with the computer on the PC side,

Click on the toolbox on the left of my phone.

There are also resource backup, data recovery, file management and so on.

Click Data Backup to back up the segment you want to back up.

Generally, it can be backed up to cloud disk and local disk.

Don't bother, it's easier to find it by backing up to a local disk.