It would probably be safer to wait until spring, as we have little time for roots to re-establish before the ground might freeze (or at least until growth slows even more); un-established root balls are more easily heaved out of the ground and killed by desiccation during temperature swings in winter. Our Growing Strawberries in a Home Garden web page recommends planting in either spring or replanting (due to renovation of the bed) right after the end of the harvest in the plants' second year.

Miri

You're welcome!