RTMP server using ffmpeg
You can use FFmpeg as an RTMP server as following
ffmpeg -f flv -listen 1 -i rtmp://localhost:1935/live/app -c copy rtsp://YOUR_RTSP_HOST

Notes:


-listen 1 makes FFmpeg act as a RTMP server when used with RTMP protocol
Use rtmp://localhost:1935/live/app as the RTMP server url on the source 
You can set any playpath rtmp://localhost:1935/any/thing and any port
The main advantage with this way is simplicity, the disadvantage is server stops if source stopped or had encoding errors
The other option is to use nginx with nginx-rtmp-module