I re-did the chart with Regiomontanus houses. I haven't seen whole signs used, yet, to find anything lost or missing or stolen.
The Moon leaving a trine to Jupiter shows that it was lost be moving and reorganizing things. Because Jupiter is in the 10th, I would think that it was reorganizing and moving things about in the main room of your house, a workroom or office. In Airs signs would indicate a place where people were/are and that it may be reorganization of things high up, on a shelf or in a pocket or hanging, like in a pocket of something in a pocket on a hanger.
Venus seems to support this as she too is in an air sign.
Air signs are west so, it may be west in direction.
I believe it is indoors because the main significator, Venus is angular and the ruler of the 4th is also angular. Also, the Moon is in the 2nd house so, it is still somewhat, in your possession.
The Moon applies first to Mars before it can get to Venus. So, as the Moon can also signify a "wondering" item it would seem to describe it in a place that may have sharp items or something hot, medical items or first-aid, a fireplace or items related to war or blood.
Mars is also the dispositor of Fortuna, so Mars is playing a roler here, telling us where the ID may be. Mars is a difficult one because not much in many people's houses relates to Mars except things hot or sharp, like knives, scissors, knitting needles, pins, etc. and that usually narrows it down to the kitchen or bathroom but, I do not think thhat is the case here.
In short, look on shelves or things that hang, upper rooms, a main room, possibly with games and where people frequent and indoors, west and near something sharp or hot.
Good luck and best wishes.