The fiber connectors are quite sturdy to insure accurate alignment and to eliminate loose connections. They can be removed and reconnected, however you want to make sure both ends are kept clean while disconnected.
During install, Verizon uses dust caps to keep the fiber ends clean until the connection is made. If the dust caps are still present, you can re-use them. Just make sure they are clean.
Note that different models of ONT may be easier or harder to move. If you post the model number, we might be able to give you more details.
If you're at all concerned about doing this yourself, contact Verizon. I suspect the will be happy to do this, although they will most likely charge for a technician visit (probably around $100).
Good Luck.