There is no ‘ifr registration’. What you need to see is in the Phase 2 operating limitations (which must be on-board), the words, “Limited to VFR unless equipped in accordance with FAR 91.205...”.
If those words are there (and you have the required equipment) then you’re “approved” for ifr. If those words are not there, you must petition the local FSDO to change the op limits and put them there. Normally not too difficult.
BTW, if you want to fly after sunset, there should be similar words (“day only, unless equipped iaw FAR...”).