Dear @Saim be,
Thank you for sharing your question with the Wefugee Community!
Unfortunately, you are not allowed to travel outside of Italy as long as you are in the asylum process. Please have a look here for more information on travelling as a acknowledged refugee in Italy.
Therefore, your girlfriend would need to travel to Italy for a marriage for the time being. The process of a marriage in Italy was discussed on this platform earlier already. You may want to check the following thread, for example:
Can Asylum seekers get married in Italy?
I hope this helps and do not hesitate to get back to us with any further questions.
All the best,