[mothered]

I've done it all and it's been delivered by FedEx, the reply given was they take these thinfs very seriously and will conduct an investigation with photographic evidence and geolocative data, and they'll report it to the police.

Under the circumstances, their reply Is standard procedure.

Geolocation data cannot be used to verify that "you" received the package and although It only confirms the address, by no means does It conclude that the driver dropped It off at the time of delivery. Put simply, the driver scans It when It reaches Its destination (and It's recorded as the delivery point), but who's to say that the driver himself didn't take the package to another address thereafter? Or perhaps steal It? I've personally experienced both events quite a number of times.

As for their photographic evidence, you've got that covered.

They asked for me to ask neighbours before continuing with the above. What shall I do?

That's a very positive sign meaning at this stage, they have no evidence of the whereabouts of your package, hence their request to ask your neighbors.

Do exactly that.

If it ever comes to that and they come a Knockin - police that is, and/or anyone else the flatmates might answer it and say otherwise which obviously can't happen..

What do you suggest?

It's up to you to organize your environment with your flat mates.