Auto Fn-lock logitech k380 keyboard

First find out the device name

grep -FH "HID_NAME" /sys/class/hidraw/hidraw*/device/uevent

Then send msg to lock/unlock Fn key

echo -ne "\x10\xff\x0b\x1e\x00\x00\x00" | sudo tee /dev/hidraw[num] # lock
echo -ne "\x10\xff\x0b\x1e\x01\x00\x00" | sudo tee /dev/hidraw[num] # unlcok

Automatic Solution

Create a file /etc/udev/rules.d/70-logi-k380.rules with the one of following lines

ACTION=="add", SUBSYSTEM=="hidraw", KERNEL=="hidraw*", RUN+="/bin/bash -c \"if [[ '%p' == */bluetooth/*:046D:B342* ]]; then echo -ne '\x10\xff\x0b\x1e\x00\x00\x00' > /dev/%k ; fi\""
ACTION=="add", SUBSYSTEM=="hidraw", KERNEL=="hidraw*", SUBSYSTEMS=="hid", KERNELS=="*:046D:B342.*", RUN+="/bin/bash -c \"echo -ne '\x10\xff\x0b\x1e\x00\x00\x00' > /dev/%k\""

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Based on answers below this question