no one wrote down the serial number anywhere or has photographs ?...everyone right now should write down serial numbers take pictures and put I.D. marks hidden somewhere on those important or expensive instruments.
Without the serial number and pictures, there is no real hope of recovery. Thousands of Pete Seeger banjos were manufactured over the years. I personally had Pete autograph the heads of several I owned over the years, so that can not be used as a positive ID on the missing banjo.