it could be wild garlic or 3 cornered leek. a photo would identify it but the treatment is the same. Don't let it seed is the first thing. Then dig out as much as you can, the bulbs go down quite a way. then spray or water with a systemic herbicide such as Resolva, Round up etc
It needs to be systemic so it will enter the bulb and kill it. These wont harm the woody shrubs if you don't get it on the leaves. For the herbaceous plants you could cover with a bucket before watering the wild garlic. for leaves that are in the foliage of other plants I have used a paint brush in the past and dosed the leaves that way.

hope this helps.

I don't know about Resolva, but RoundUp works best through the leaves. Applying enough to work through the soil will damage surrounding plants. I would put on marigolds, get a washcloth or sponge, spray RoundUp (or better equivalent) on the sponge or washcloth until it is wet, but not dripping, and gently wipe the weedkiller onto the leaves of the onions a week BEFORE digging them up. Avoid getting any on anything that he wants to keep, and be ready to repeat once a month through the next 2-4 growing seasons. As Sbg says, Keep it from going to seed. If his neighbor has it, too, Keeping it from creeping over will become an annual ritual.

Just a long shot - there has been lots of controversy about whether glyphosate (eg Roundup) leaves a residue in the soil. Best to avoid growing anything edible where you have used it.