I have a Philips 43PUS8556. Its remote has a qwerty keyboard on the back that works fine with the TV's own Android system but the Firestick connected to it doesn't do anything when I try to type (rest of the remote works fine). Is there any way to make it work?
No clue really but see if the remote has a pairing mode. It may be a Bluetooth Infrared hybrid. If it has a pairing mode option you may be able to pair it to the fire stick as a Bluetooth keyboard. Most android OSs have mouse and keyboard support built in.
Edit look under the batteries and see if the remote has its own model number and search that model number + pairing mode.
Alternatively down load the FireTV app on your phone and just use it with the tv it has a keyboard you can use.
No. It's controlling your Fire TV Stick via HDMI-CEC and that protocol doesn't transmit QWERTY keyboard info. It works with the TV because its connected via Bluetooth. I don't know of any Bluetooth TV remote that allows you to pair it to multiple devices at the same time so you won't be able to use the TV's keyboard with the Fire TV Stick. You'll need a separate Bluetooth keyboard, like the Logitech K380, for the Fire TV Stick.