Hi, if it has the same amount of gears usually 3 then you will have no problem at all swapping them over, now as long as the frame thickness is the same or the new derailleur can take up the slack on lock onto the frame securely then you will have no problems what so ever.

The only thing you need to make sure you get right is the allignment and the cable tension correct so it changes the gears as it should do, it may take some adjusting but its not to difficult to do, as long as you run the cable correctly and you have the cable pulled through enough then the gears should change just fine.

once its fitted you can then adjust the cable after to ensure it is changing gears properly, the only problem you may have is if the cable is stretched or damaged as this can cause the gear change to be slow so if you are unsure of the cable then replace with new as its costs next to nothing for a new cable, but apart from that you should be able to do it no problems as its an easy job to do, just make sure the cable runs where it should do if you do change the cable as long as you do that you should have it done in couple of hours.

let me know if you have any problems ok