2016 Mustang Sync3 1.0 updated to 3.0 and no Apple Carplay!

They are indeed the same part.

HU5Z-19A387- *
HU5Z-19A387-A (BLUE BACKLIGHTING) Ford (Wide 1 USB-A Port, w/Pass Through)
HU5Z-19A387-B (BLUE BACKLIGHTING) Ford (Wide 1 USB-A Port, w/Pass Through)
HU5Z-19A387-C (BLUE BACKLIGHTING) Ford (Wide 1 USB-A Port, w/Pass Through)
Interchange Part Number:
HU5T-14F014-AA, HU5T-14F014-AB, HU5T-14F014-AC, HU5T-14F014-AD, HU5Z-14F014-BB
2016-2019 Ford Mustang
2016-2019 Ford Focus
2016-2019 Ford Explorer
2016-2017 Ford Transit

Media Hub, CarPlay Compatible - 2015-2020 Ford/Lincoln - SYNC 3 - Ford / Information - CyanLabs Official Community

Once on 3.0.20204 you should be able to have CP by just plugging the phone in with an Apple cable. Is there an issue you are experiencing with CarPlay?