Yes you could have a friend for life, it is one of those plants that grow from the smallest bit left.
You have to be persistent to remove it. You can grass the area and mow regularly for some years, cover with black polythene and leave covered for several years, hoe/hand weed on a weekly basis removing every bit you can see.
Do not dispose of in domestic compost as you will spread it. Send off site as green waste or drown in water butt for at least three months until a black, smelly, slimey mess.
Ground-elder (Aegopodium podagraria), also known as Bishop's Weed or Goutweed, is a rhizomatous perennial in the Celery Family (Apiaceae). It is native to much of temperate Eurasia and the islands of Japan and Sakhalin, though it is considered introduced in the British Isles, as well as North America. It has a well-deserved reputation for being invasive in both its native and introduced range.