You should provide more specific details. Where & When are you starting? Finishing? What type of battery?
Even if you find such a rental service, I don't think for 3 months you would find the cost to be favorable. You probably are better off to arrange a purchase and resale in advance, maybe with the help of members here. As there is already a high cost for such a trip, I would avoid the potential disappointment of problems with a used battery (unless a trusted history), and start with a new and hope to get a good resale value after. Purchase could be arranged ahead at a bike shop near your start. You could sell as a private transaction through eBay or here at EBR:
https://electricbikereview.com/forums/forum/fsbo/
and to help with shipping for the sale:
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I've considered how to deal with the same in reverse, coming from California to Europe. My bike, however, would subject me to a 30,000 euro fine in France or complicated registration and insurance issues, and last time I didn't find the 15mph e-assist limit of rentals there suitable for long range touring, so my excitement of such an idea has diminished.
