Thanks for all that additional information, which by the way further substantiates Jimmy T’s comment that the whole situation from the Owners Corporation paying for a split-system air conditioner to benefit just one Owner, to it installing that on your balcony is just plain ludicrous!
As you did earlier obtain a legal opinion, you should strengthen your letter to read something like:
Please be advised that on the on basis of legal advice, I advise both you and the Owners Corporation that the Executive Committee’s decision to purchase and install a split system air conditioner to service Lot X and to install the outdoor component of that on my balcony was incorrectly made, and not in accordance with the requirements of the NSW Strata Schemes Management Act (1996), and particularly with the provisions of its Section 65(A).
Therefore, as an alternative to me applying to the NSW Civil and Administrative Tribunal to have the Adjudicator’s ruling set aside and also to seek Orders to have the Owner of Lot X, and in default the Owners Corporation, restore the Common Property to its original state by removing the aforementioned air conditioning system and its ancillary pipework (the “works”), I am allowing seven (7) days from the date of this letter for the Owner of Lot X and/or the Owners Corporation to make suitable arrangements with me to enter my property for the purpose of undertaking those works.
If those arrangements are not made within the timeframe prescribed, then I shall concurrently make arrangements for the works to be undertaken and for all items once removed to be properly secured and made available for collection by the Owner of Lot X or by a member of the Executive Committee, and make the necessary Applications to the NSW Civil and Administrative Tribunal as indicated and including a ruling that a reimbursement of my costs to have the works undertaken be made in equal portions by the Owner of Lot X and the current Members of the Executive Committee.
Remember though, as the above is what I would include in a letter, just make sure that you are totally comfortable with whatever you may yourself write.