Gilera Nexus 500 overheated after alternator change (stator)

Moin, I have been having problems with my Gilera Nexus for a few weeks (BJ. 2005 with 44t km). It all started with the fact that the battery could not be charged during the ride, so that you could only move the scooter with regular charge of the battery. After it was unfortunately not on the voltage converter and a change did not bring any improvement, and the scooter was only good for about 70-80km range, there was still action needed. On Saturday the exchange of the alternator (stator) was then on (from my dad who said he gets it, has been screwing on motorcycles for 50 years) After that, the voltage went back, slightly over 14V during the ride, battery recharges again, all so far okay… except that the scooter gets so hot after 8km that the temperature indicator flashes and only shuts off and waits for a way out. The thermostat was tested and bridged, both brought no improvement. From the feeling there is no pressure on the lower hose, so there is no circulation. The assumption is that it is either what is in the area of installation of the alternator or in the area of the water pump (pump rotates, although felt wrong, the shovel wheel does not take the maximum amount of water with it because of its shape, but is unclear to us as to how this can be possible or if that is even possible). Since I am a bit desperate, I am grateful for any idea. What could have gone wrong when the alternator was installed, that now there is no going Kühh Is water flow more present?