Because your girlfriend is a UK citizen, she can come here without a visa. (Though, as of March 16, she will need an eTA to travel here.) The simplest option would be for her to come here to visit you and then you can marry.
Then, you can sponsor her “inland” (i.e. she stays here) or “outland” (she goes back to Northern Ireland). Unless your theft was a violent crime, it’s unlikely that you are ineligible to sponsor her.
The advantage of “inland” is that you are together (and she can apply for an “open” work permit). The disadvantage is that you cannot appeal a refusal. The other disadvantage is that the processing time is currently 26 months.
The advantages of outland are that the processing time is 12 months (at the moment) and you can appeal a refusal.