Do you have an employment contract in place? My gut feel is that the commitment to make them a partner, if not in writing, is just a non-enforceable promise, and even if he was considered a partner, wouldn’t have an impact on the employment relationship.
If they are genuinely saying they have worked and have not completed (and by not completed , I mean didn’t even clock on for work at all) you’d still need to go through a disciplinary process, give them notice of meeting to address the concerns, give them an opportunity to respond, then consider that info and make a decision as to what you want to do
If they haven’t been employed for more than 12 months (I’m assuming you have less than 15 employees), then they don’t have access to unfair dismissal (doesn’t stop them making you attend an unfair dismissal conciliation though, which may give you the opportunity to give them some money/ sign some settlement terms), but you can raise an objection to it going any further from there and the Fair Work commission won’t want to hear it and will stop their claim progressing further. The objection is pretty simple to lodge and probably doesn’t need legal assistance to prepare if you are somewhat savvy.
I think the risk is pretty low tbh based on a couple of assumptions, but definitely consult with an employment lawyer or consultant so you can tell them the full story and get their perspective.
I’m happy to chat further over DM if you want as this is in fact my area of expertise.