Purchased the phone from AT&T. There is an AT&T Software Update link in the Settings page. The About page for System updates is to install the build file(s) manually downloaded to the SD storage card. No luck in finding any build version(s) for this Z-958 phone.
As the last resort, after I had done everything that I could to run the software updater, I did several hard resets to attempt the OTA software update from Baseband version: Z958H01 and Build number: Z958V1.0.0B18 with no success. One poster mentioned three tries of hard reset with success without any method/process. There is plenty of internal storage space -- file is approximately 1.2 GB in size, which requires Wi-Fi connection for downloading.
There are two other builds -- previous versions required -- to update before the final update to build number: Z958V1.0.0B26. See: https://www.att.com/devicehowto/tutorial.html#!/stepbystep/id/stepbystep_KM1127815.
Customers are aware that it is up to AT&T to push the Android Operating System to their specific device. Yet, ZTE Website should provide several build files for manual download for the specific device of the customers.
Because of the lack of support from their Website or care for our SECURITY, I am considering to switch to another company and destroy the ZTE device so that others would not have to go through wasted time and efforts. Second, to recommend family/friends not to buy ZTE products. My partner has Moto G4 and she recently upgraded to Android Version 7.0 Nougat. Note: rooting this device permanently is impossible.
Should I succeed with the update(s) soon, I will add to this post.
ZTE ZMAX Z-958
Baseband version: Z958H01 and Build number: Z958V1.0.0B18
Android Version: 5.1 Lollipop.