Just to be clear on the legalities of this. Per s111 of the SSMA (below), as soon as work affects common property, unless there is a pre-existing by-law that covers it in detail, it will need a by-law or approval through a special resolution.
This is not a strata committee decision, it’s an owners corporation decision, to be made at a general meeting. And the terms of the request should be precise. A ‘letter’ seeking ‘retrospective approval’ is not a thing.
It would be a good idea for the building to work out agreed guidelines on air conditioning installation and location, then embody those in a standard by-law so the rules are clear for all. You may be able to find a suitable by-law template on one of the online services, otherwise (ideally) have it drafted by a lawyer. Apart from appearance, sloppy aircon installations can create water ingress problems and compromise electrical safety (ask me how I know!). Insist on full details of all contractor licences and public liability insurance.
Good luck!
An owner of a lot in a strata scheme must not carry out work on the common property unless the owner is authorised to do so—
(a) under this Part, or
(b) under a by-law made under this Part or a common property rights by-law, or
(c) by an approval of the owners corporation given by special resolution or in any other manner authorised by the by-laws.