Is there any fully Byobu-compatible terminal client for Windows?

I'm trying to use Byobu on a Linux server via SSH from Windows. I've tried with MobaXterm and putty, but some of the F key combinations simply don't work. In MobaXterm there is even a dedicated Byobu terminal type setting, but the F5-F8 keys ignore the key combinations with Ctrl. I've listed the codes sent to the terminal with cat -v. The code for example **F6** is ^[[17~, but for **Ctrl+F6**, it sends the exact **same** code. Is there any terminal client for Windows that can send distinct codes for all F-keys with all modifiers (Ctrl, Alt, Shift)?