I'm moving to a hew home. Can I remove the mezuzahs from the doorposts when I leave?
As a rule, a mezuzah should not be removed from a doorpost, leaving the room or house without a mezuzah, unless it will be put back or replaced with another mezuzah.
Thus, when moving to another house or apartment and the next tenant is Jewish, the mezuzahs should not be removed, unless there is concern that if the mezuzahs are left behind they would be discarded or defaced.
If the new occupant has his own mezuzahs and wishes to use them rather than the ones you leave on the doorpost, it is preferred that the new occupant should himself remove your mezuzahs when installing his own, or that, at least, it should be he who instructs you to remove the mezuzahs. This law is a very serious matter and should not be treated lightly. A competent rabbi should be consulted if in doubt as to how to proceed.
If the new occupant wants the mezuzahs, you are obligated to leave all of the mezuzahs in their place. If your mezuzahs are of a high quality and expensive, you may replace them with less expensive ones before you leave, providing that they are 100% kosher. The mezuzah cases may certainly be exchanged for inexpensive mezuzah covers.
You may also request that the new occupant pay you for the mezuzahs, in which case one will be obligated to compensate for the mezuzahs at fair market value.
If one is in the midst of moving and temporarily owns two homes and is actually living in both homes, or storing items in both homes, then one is obligated to have mezuzahs in both homes.