Is it permissible to eat fruit that falls into my garden from a neighbor's tree?

The fundamental principle is that it is impermissible to eat fruits owned by others without their permission, based on the Almighty's saying: "And do not consume your properties among yourselves through falsehood." An exception to this is what people customarily overlook, such as eating from someone else's garden if it does not have a wall enclosing it, acting upon the hadith (definition): "If one of you comes to a garden and wishes to eat, let him call out 'O owner of the garden' three times. If he responds, [then ask for permission]; otherwise, let him eat." In your specific case, act according to what is customary regarding leniency or strictness. The most cautious approach is to avoid eating from them unless the neighbor's consent or permission is known. Fallen fruits share the same ruling as those on the tree; if they are inside the wall or outside it and custom does not permit their consumption, they are not permissible. However, if custom permits their consumption, the correct view is that it is permissible.