The Scottish rocker, who befriended Rickman when he starred in the group's 2000 music video for In Demand, revealed she persuaded him to take the role in the much-loved films.
Once shooting began, Rickman - who played Severus Snape in the franchise - showed Spiteri the wig he was to wear, which he told her was inspired by her trademark tresses.
She tells Britain's Daily Mirror newspaper, "When we made (In Demand) we were chatting in make-up and Alan said, 'Have you heard of these Harry Potter books?'... I told him it was such a big deal and he should definitely do it. He'd already said 'yes' to the part but hadn't got his character together."
"So it was only after we met that he got his long black wig and decided he was going to be, like, my brother. That was the inspiration. He invited me down to the set and on the first day, picked up his black wig, held it up and told me it was based on my black bob from the In Demand video! He joked he was playing my ugly sister. Alan and I have been mates ever since. Whenever he's got a film or I've got concerts on and we're in the same country, we try and meet up. He's great."