Transferring non listed iphone app to another iphone?

I got a unique question for all of you.

So I have this Verizon iPhone 4S which my company gave me and charged me $400 deposit. I broke the screen last night so now if I take it to my company for a replacement, they will be charging me $400. Verizon iPhone 4S cost only $200 on Craigslist and IIm thinking about buying one

BUT

The problem is that my company phone has this one application which is of course not available in the app store.

So is there anyway of transferring that app to the new phone which IIm about to purchase from Craigslist?

A quick and helpful response will be much much appreciated.

You can try to backup to itunes then copy to new phone, however with a non appstore app that was put on my the company I would assume that still works via backup this way but not sure.