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:
Pack and ship electronics, The UPS Store has a suite of electronics retention packaging solutions that protect shipping your computer equipment. Specialty Electronics Packaging for Laptop Shipping, Tablet Shipping, Smartphone Shipping and More.
www.theupsstore.com
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.
