I'm not sure there is a set way. Someone I know was involved in a similar situation. The money was paid 6 weeks after the court case conclued, via their solicitor, to the courts office but it sat on someone's desk for 6 more months. It was only when the victim bumped into the investigating Garda and mentioned that the money had not yet been received that the oversight was noticed.
Moral of the story, keep in touch with the Gardai involved and your own solicitor, if you have one.