I do not know of any way to do it with only a single keypress.
For sending calls to voicemail directly, I make a prefix key.
The prefix key labeled "To VM" has the dial code.
*by default in FreePBX, and in your case, it would be
Then teach the operator this method:
- Press Xfer
- Press To VM
- Press BLF
This works on both Yealink and Fanvil.
This is a yealink - right?
There is no option for Prefix under type for Fanvil.