No, you can't share just by share (with its playing option as well) just by clicking on share. An error comes up, most of the time. "TypeError: FB.XFBML is undefined" - This is the error that comes up. Nothing worked as their website suggested on facebook.
So, I tried this. This is all you've to do to make sharing to facebook possible.
>> Go to URL - and remove "#" from the song.(an extra backslash will have toremoved as well, example given below)
2. Removal of "#"
3. Now share
It will appear, perfectly now (i.e. with the player).
Example of song shared through is given here/ facebook.com/muwasalat
JFYI - The song mentioned above is by Right Away, Great Captain (What a Pity). It's a nice song. Sounds like William Fitzsimmons and it's a very short song 1.40 min. long.