How do I activate Screen Mirroring on a Samsung Galaxy S5 running Marshmallow?

I have an Amazon Fire TV stick, and I'd like to mirror my Samsung Galaxy S5's display to it. **It works fine with my old Galaxy S4** (just tried it right now), but I cannot get it to work with my Galaxy S5: The "Screen Mirroring" option just does not seem to be available anywhere on the phone. It's a non-rooted Samsung Galaxy S5 with the latest OTA update (Marshmallow) installed. --- **What I've tried:** I already googled for s5 marshmallow screen mirroring missing and tried the following recommendations: * Pull down the notification shade, click Edit and activate the Screen Mirroring option. On my device, *there is no such option*. * Click "Quick Connect" on the notification shade and register the TV stick as a TV device. Tried that, but the only option I have is to *"Share content"*. It does not offer to share my screen. Here are two a screen shots as proof. I'm sure I'm missing something obvious...