Law arrived from Rotherham weeks after watching Motherwell lose to Celtic on television in the 2011 Scottish Cup final.
The 24-year-old has since helped the Lanarkshire side to a third-place finish in the Clydesdale Bank Premier League, the position they currently occupy, and sampled the Champions League and Europa League qualifiers. And a cup run and trip to Hampden is one of his next goals.
Motherwell will secure a fifth-round trip to Easter Road to face Hibernian if they beat Aberdeen in a replay and Law is set on keeping his ambition of making a cup final alive.
"The lads speak about it now still, how disappointed they were but what a great occasion it was," the former Sheffield United player said.
"Coming up here, that's a big attraction, the cup runs and playing for European places because in England it's tougher. Only the elite clubs in England get the opportunity to play in cup finals and semi-finals.
"It's something I would love to do, play at Hampden, something I would love to experience. We are just looking at this game and trying to get through it and if we do we will look at Hibs, but it's definitely a goal of ours, to get to Hampden this season."
Manager Stuart McCall believes a run to the final could help persuade his many out-of-contract players, including Law, to stay beyond the summer but Law is not thinking that far ahead.
"Nobody has spoken about leaving," said Law, who scored in Saturday's 3-2 win over Ross County. "We have so many big games coming up and we are concentrating on them.
"I can honestly say I have not given it a thought. Anything can happen between now and then so it would be stupid to say you were leaving or staying, and you don't know what the manager is thinking. It's just the football at the minute."