Q. Is removing, taking care and storing the suka properly, so it will in good condition and ready for the next year, considered already as the mitzva of building a suka? (For the purpose of osek bemitzva patur min hamitzva or zrizim makdimin and doing the mitzva promptly.)

A. Shulchan Aruch (O.H. 641: 1) rules that one does not recite a brocho when building a suka, since the mitzva comes to completion only when one sits in it (Mishna Berura ibid.1.) Poskim deduce from the above, that there is indeed a mitzva in erecting a suka. However. Biur Halocho (ibid 1) maintains that it is only when this is done within thirty days before the Yom Tov.
Horav Shlomo Miller’s Shlit’a opinion is that disassembling and storing the suka parts is not a mitzva for the purpose of “osek bemitzva or zerizin makdimin”

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a