Identification: Identify this sad mystery plant?

Hello, thanks for taking the time to view my question. Recently I visited a local florist, and he gifted me this plant. He said he had no idea what it was and he was having trouble keeping it alive, but "maybe I would have better luck".

Initially I thought it might be some kind of african violet, but my experience has been that those have fuzzy leaves. The leaves of this plant are smooth and shiny. When I got it it had been badly over watered and I had to clean a lot of mouldy debris from the soil. The stalks are soft and fleshy.

Here's a photo of the leaves, the stems, and the plant on the whole, with a standard sticky note for size reference. I'd be grateful for any help you could offer.

 

Peperomia, perhaps.

 

Amazing! After some googling, I think it might be a Peperomia caperata. I'll follow care instructions for that plant and see if it helps.

Thanks a lot!