Will storing used speakers for 1 year damage it?

I am seriously considering a pair of used Nautilus 803’s which are being sold for a good price. However, I won’t be able to use them until I move to my new place which is about a year from now.

Question – will storing a used speaker for a year damage it? If no, what is the best way to store the speaker?

I hope not, I have some that have been in storage for a year. Climate control is the best way to store--you don't want radical humidity or temperature changes. Also, when you do get the speakers out you will have to break them in much like a new pair.
Store them in a dry, medium warm place, make sure that no UV light might affect the chassis. Sit back as often as you can in the hassle of building and/or moving close your eyes and look forward to getting them out and running!
Good luck!
Try to store them in a climate controlled environment. Extremes of temperature and frequent temperature changes may effect driver surrounds and high humidity could corrode binding posts or other contacts. Also, try to cover them or store them in their shipping container to protect them from dust.