Dry cleaning and alterations shops must suffer from this a lot; these are the visible symptoms of the chaotic lives some people lead. Abandoned bikes and cars and unpaid bills are all the same; people forget, they move, get ill, die, go to prison, have a breakdown, breakup, or just can't afford or be bothered to collect the item.
In this case the customer probably can't afford the repair and has just gone and stolen another BSO. I would text him a warning that after three months you are going to sell the bike. Deduct your costs and keep the rest to give back if he ever shows up and your conscience is clean. Take photos of the bike and the bit you've repaired and keep them with the cash in an envelope so as to settle any dispute.