I grow my strawberries in hanging baskets, one plant per basket. This solves the problem of slugs, etc. The problem I found was propagating new plants from the runners. I used to cut the new growth off the end and just pop them into a small pot with soil but the success rate was only about 30%, so I came up with a novel idea to get more plants. What I do is take about a spoonful of compost, place it just under the leaves on the runners and wrap it in cling film around the runner. I secure it with a small elastic band and leave it hanging down for about 10 days until it roots, cut the new plants from the runners and plant them on. The cling film keeps the compost moist long enough for them to root and I now have a 100% success rate. I suppose sphagnum moss would do the same but compost works fine for me.

Thanks Myron, I appreciate the reply, but it didn't really answer my question. What will be the best time to move the plants that are currently growing in the ground in addition to the new plantlets. I intend to use raised bed type containers which will fit into the space currently occupied by the 30 or so ground growing plants.

I would move them now, they should be ok. The new plants might establish well enough to fruit this year. Mine have with the hot weather that we are having over here in the UK. If not then they should over winter ok and produce a crop next year.

Thanks Myron. I'll give the plantlets a couple of more weeks to "take" and then have a go at moving them all. I'm not bothered about the new plants fruiting this year; I'm just about strawberried out!