We reported before that Samsung will be launching a Galaxy Core Prime Value Edition device with Android 5.1 Lollipop Pre-installed. Today, one of the Original Core Prime variants got the 5.1 update,  T-Mobile Galaxy Core Prime (SM-G360T) official Android 5.1.1 Lollipop firmware is Available. The Original Core Prime should also get the same update later this Quarter (Q3,2015 - July - August - September) in various regions.

The Galaxy Core Prime official Android 5.1.1 firmware packs a new TouchWiz UI with Material Design, New Notifications Panel, New Widgets, Updates Samsung Apps, New lockscreen, Security fixes, Improved Wi-Fi connectivity, various bug fixes and performance improvements. T-Mobile included all the 5.1 update details in this User Manual [TMO_SM-G360T_Core-Prime_EN_UM_LL_5.1_OF7_R4.PDF] on its support page.

Use our Odin 3 Tutorial to know how to flash this Official Firmware to your Samsung device, and don't forget to follow Samsung's Official updates Page to get the latest updates status.