I grow antique strawberries on my homestead. Yes, they're not a large as modern strawberries, but their taste is awesome. They have grown on my land since before I bought it, but they need to move around to new areas every 3-4 years.
At the moment, I'm having to grow them in large containers because our deer like strawberry leaves as much as I like the berries. Strawberry plants tend to die if every one of their leaves gets deer browsed.
The absolutely easiest way I've found to move strawberry plants is to fill a bunch of pots with good dirt (homemade compost, mixed with dirt, biochar, and a bit of coir because of our summer drought)
I put the pots into a bin so it's easy to water them and they don't get tipped over.
Then I lead a runner into a pot and put a friendly rock on top of the stem to keep the stem in the pot and to act as a bit of mulch on the surface to help keep the pot moist.
The top right baby was rooted earlier this year and has been separated from its mother plant already. This is just the safest place to put it until late fall planting.
The other five pots just got set up today. I try not to get too far ahead of myself, but I am thinking I really need to set up another group of 6 as my daughter in law has discovered she really likes strawberries!
For 30 years, these lovely strawberries have been self replicating!