I have a 2003 Mitsu montero 3.5 sport w/awd. Transfer lever stuck in 4h and my mech friend tried to help but dropped

Hi,
I know this sounds silly, but if you aren't 110% certain it went inside, take a look around under the vehicle and reach up from underneath to feel around on the top of the transfer case just on the off chance it did not fall in, but rather off to the side.
Unfortunately if it did fall in then the magnet is going to be your best option here, due to the way the transfer case is constructed. There aren't any really easy access point to get in. If it is definitely inside, your best bet would be to get some assorted extension magnets like you have already tried but in varying sizes and preferably with shields (you can get these with small stainless sleeves that prevent the side of the magnet from sticking to everything).
There is one pan cover on the passenger side for inspecting the chain that is roughly below the shifter area. You can try removing this to see if you can get a better angle in there... it is unlikely the bolt fell down to this spot, however removing it will provide you additional areas to insert your magnet. You will need to drain the fluid out before removing the cover though.
If you absolutely can not reach it and are certain it is inside, your only option is going to be to pull the transfer case and split it for removal. This is DEFINITELY not what you want to have to do though... it is a ton of work, and heavy work at that, certainly not suitable for doing on the ground if avoidable, and you do not want to drive the vehicle in the mean time until you are certain of the bolts location, as you could very easily cause catastrophic damage to the transfer case if you drive it and the bolt is in an undesirable position.
I am attaching below a blow up diagram of the case showing the pan cover (highlighted) and the rear case cover (highlighted) which would be your access points if the magnet does not have any success.

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