Hello,
could anyone give advice on how to move an IKEA matress from one apartment to another?
A name or a phone number of a suitable moving company would be perfect.

Thank you.

find several friends help and call taxi company 021-96811(do not know whether they have english service), they can dispatch a moving truck for you. Note: the driver does not help you on the moving.
This is the cheapest way to moving a matress.
good luck!

Got it.