If he doesn't want to trim, one solution to consider is digging up a space (about 8" will do) from the fence into his yard. Fill the space with landscape fabric and several inches of small stone or mulch. Tamp it down level with the lawn. You can then mow away from the fence and there's no need to trim. Roundup is OK but doesn't look that good. If he does trim along the fence he needs to be careful not to damage it. A powerful trimmer can cause damage to vinyl. This is not an issue that's worth a confrontation with his neighbor.