The ASC in Saturn makes your significator Saturn in Leo technically in the 7th house. Neptune Rx on the ASC is a big uh-oh! There's illusion, delusion or deceit involved. The offender is signified by the Sun, the ruler of the 7th. Interestingly, the Sun is also the almuten of the 3rd house, your neighbors. The neighbors also share the same sign ruler with the police (10th house – authorities).
The Sun is in major dignity essentially and accidentally. I say the offender is quite safe and sound and in a very comfortable environment. Mars is peregrine in Virgo in the radix 8th where it has major accidental debility. It in own turned chart, however, it still is peregrine, but has major essential dignity by being in the 11th.
The neighbors are equally peregrine as they are also signified by Mars. In both the radix and their turned chart, they are in accidental debility. However, if we use the Sun to signify them, the significator is in the 7th and their turned 5th having accidental dignity in both cases. Using the almuten like this shows major affinity with the offender.
There is no application or translation or collection of light between any of the significators involved. I think no one will be able to catch the offender. The Moon, a co-significator or you and the question, is heading towards an opposition with Pluto Rx in the 11th house. Pluto is a modern malefic that is even more vicious here by being Rx. The 11th house rules friends, hopes and wishes, and organizations. I don't know if that means anything.
The last lunar aspect is a sextile with Sun, the significator of the offender. I cannot interpret that as "yes, eventually" with everything that the chart has shown so far. Between the Sun in dignity and receiving the moon and the Moon itself peregrine, I say the thief may very well get away with this.
I wonder what the affinity between the neighbors and the offender means. Maybe they know him. It would be too far out there to imagine that they had something to do with it.
Keep in mind that I don't do this kind of horary very often. I do relational horaries mostly. So don't take what I say on this as guaranteed, and please keep me updated on how this goes. It would help me learn about horaries of this type.