That's a fascinating thing, and you're more than half-right, I think, in saying "it looks as if it was meant to be". It loooked vaguely familiar to me and a bit of research (in Casques de Combat, ELMETTI, and the WWH website) shows that there is a variant of the M56 with an add-on set of neck-and-earflaps with chinstrap specifically for motorcyclists. The kit is remarkably similar to the flaps/straps of the wz63 para helmet which was of course bought in by the DDR. It seems to me that this may be either a bit of inspired conversion by someone with access to both helmets (in service, at the time, I mean), or actually an officially sanctioned upgrade. Alternatively it would have been done by some herbert who was vaguely aware of the original conversion kit and assumed it was a wz63 liner complete.
So, something at least deeply rooted in reality, possibly not a frankenhelmet at all.
Here's a somehwat computer assisted translate of the WWH writeup taken from here http://world-war-helmets.com/fiche.php?q=Casque-Est-Allemand-Mle-56-66 where you will find some pics.
"Other than the Polish Wz 63, originally intended for paratroopers of the NVA, and used by some motorcyclists units, no helmet was not designed to equip the couriers of the NVA, who then used the M56 and M56/66 model.
In order to best protect motorcyclists, an accessory was created to complement the helmet model 56 and model 56/66 to adapt for use on two wheels.
Made of leather with a glossy black outside, this accessory is lined with cloth inside, sewn along the entire edge. The closure consists of snaps, spread among three left (male) and two right side (female). This complete closing the strap of the helmet, which can be inserted in two leather loops sewn on the sides.
The front edge of this accessory is lined with two strips of felt to ensure fitting against the cheek of the wearer and thereby prevent the air ingress. The sides have two pieces of leather sewn with an open edge to allow for adequate hearing.
The part covering the neck is lined with a rubber band to ensure close fitting. A tongue of leather, resealable with a snap, stabilises goggles, necessary for riding a motorcycle.
The attachment of this assembly to the helmet is done by inserting the existing chinstrap loops, which are inserted in four slots of the accessory and the fixing is through four tabs, riveted to the edge."
Either way, you have a genuinely unusual and possibly quite rare helmet.