Can you move wild ferns, and is this really bracken?

This looks like bracken, with its airy, finely divided fronds and triangular outline. It can be moved, but in late August in Sweden it is better to wait until the plant is more clearly approaching dormancy, or move it in early spring before new growth begins.

Dig widely rather than deeply and include a section of rhizome, as bracken spreads underground. Replant straight away at the same depth. You describe steady moisture and partial shade, which suit establishment. Water thoroughly after planting and keep the soil evenly moist at first, especially in a dry autumn.

Expect the fronds to look tired after moving even if the roots survive. To reduce stress, you can remove some foliage at the time of moving. As bracken spreads readily, move it only somewhere you really want a wild, spreading fern.