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In theory, since international LTE model GT-i9505 and T-Mobile Galaxy S4 SGH-M919 share the exact same hardware as AT&T Galaxy S4 SGH-i337, it should be possible to install GT-i9505/T-Mobile custom ROMs on your AT&T Galaxy S4.
Well, I tried it today and it works just fine. You will need to install a custom kernel such as KTweaker kernel after installing ROM though to bypass the locked bootloader on your AT&T Galaxy S4.
For Canadian SGH-i337M users, you don’t need to install a custom kernel, just install any GT-i9505/T-Mobile custom ROMs and they should work out of the box but do check for modem in the ROM file also.
To install GT-i9505/T-Mobile custom ROMs on your AT&T Galaxy S4:
First, make sure there’s no modem.bin file in the custom ROM zip file. You can easily check this by opening the ROM zip file.
Second, make sure you are using GT-i9505 custom ROMs NOT GT-i9500! GT-i9500 uses different Octa-core CPU, meaning you can hard-brick your phone so just make sure you are using GT-i9505 or T-Mobile custom ROMs.
Third, you can use TWRP or CWM recovery. If you get Status 7 Error during install, you need to remove asserts using this method.
What is a Custom ROM?
A custom ROM is a custom, modified operating system that you can install on your Android device. Basically it's like installing Windows OS on a Macbook. By installing a custom ROM, you can bypass stock factory settings like locked hotspot tether, install new Android versions early, or even convert your phone into another OS.
With a custom ROM, you can really maximize the capabilities of your smartphone by adding custom features that have been developed by open source developers.
How to Install Custom ROMs
First, you will need to root your device, if it is not rooted yet, follow our root tutorial and root your phone.
Once rooted, you should have TWRP installed on your phone. Installation of a custom ROM is easy if you learn the basic of it. If you don't know how to install custom ROMs using TWRP recovery, see our tutorial on How to Install Custom ROM using TWRP!