There is no specific serial number prefix that distinguishes a black body from a chrome body. Both finishes were produced concurrently within the same numerical blocks.
Toward the end of the FE2’s life cycle, Nikon switched from the titanium honeycomb shutter to smooth aluminum blades (standardized in the later FM2n). Units with serial numbers starting with 242 or higher are more likely to have the aluminum shutter. Why the Shutter Material Matters nikon fe2 serial numbers
On the Nikon FE2, the serial number is engraved on the back of the top plate. Directly behind the film advance lever. Format: A simple 7-digit numeric code. There is no specific serial number prefix that