Drag rectangles with labels in tandem

[koreańczyk]

Hello!

I have some draggable rectangles with binded labels to them. 
Sometimes I want to have those labels to be static.

I thought about two possibilities:
1) Make invisible marker and move it when rectangle is dragged.

2) Make labels from Leaflet.label display as static ones

I tried somehow to drag GroupLayer, but it seems it's not possible.

Any there any good solution to this?  I'd be very happy to see some feedback on this. 

Cheers!