Modern Vespa

Hi. My other half bought a Vespa gran tourismo. 2003. It was a 200cc but the last owner had engine swapped for a 125 for their kid to use. So we had it running for about a week and then it started slow cranking I replaced pretty well much all the major factors ie battery st motor reg rec
It started to crank faster but would
Not start. There is spark at the plug
I took it to a Vespa specialist who had it for a week. And has pointed out a few things various washers missing and a chunk of the crank case missing. Also the coolant was almost out . His verdict. Prob. Needs a new engine.
However we are struggling to id the engine that is in it he stated that they used 2 or 3 different ones for this model and year.
As the one in it is def not the correct one.
So I need to look for another engine. Does any one have an idea of which. Vespa / PIAGGIO engines will fit the GT 200 frame as I am struggling to locate one.

I am almost certain that there was only one engine fitted to the Vespa GT125. They turned injected around 2007. There is only one carburetted engine from the early days till then.

This is an ad for a later injected engine https://www.ebay.co.uk/itm/236206362827

This is the one you want
https://partbike.co.uk/p/spare-parts/mechanics/engine/engine-piaggio-vespa-granturismo-125-2003-2007

This page from easyparts lists the engine numbers. M314M

https://www.easyparts.com/models/Vespa-GT-(Granturismo)-125-m2346