ok, so far ...
Thanks for your answer,
I already replaced a battery in my MIO 320 Navi. I got it with ebay - specified for the MIO.
The problem is the connector, I don't know if there is a standard. When there are 3 contacts, ok. At least I would cut the wires and solder the old connector to it.
I will try to open the case and have a look at the battery.