Write or type a letter to your neighbor explaining that you’d like to help them make their fence safer, then leave it for them if they’re not home when you go to drop it off. Provide your name, a way to contact you, and be polite. Don’t make moves to alter their fence without them; changing your neighbors is expensive and good will is priceless.
If it’s a chain link style fence, with the exposed ends twisted together and jaggedly facing up, a top rail with fasteners is likely to be the easiest to set up. If there’s a fencing installer locally, try calling them up and telling them about it, then ask if they have the means to fabricate or modify a top rail to work for what’s going on. If you have the means to make a jig for an angle grinder you may be able to cut appropriate openings in the top rail yourself and secure them with ring clamps or appropriate hardware for connecting them to the upright posts. Wooden toppers might be less expensive to purchase or fabricate but will have their own upkeep needs - a router with a channel bit or a table saw with a dado blade could make short work of the recess needed to cover the sharp parts of the fence, and conduit clamps could be used to secure it in place.