Can I move an established tree fern?

This is what I have found.

Apparently they dont have a big root system but they are pretty resilient. They say to just go in as deep as you can when lifting it. It definitely needs wet soil (keep it moist after moving it) and position in shade, facing south. Then nature will take its course, hopefully all will be well. Good Luck

Sound advice from Cherylrp - as much root as possible.
Additionally, don't forget that these plants will be most happy when immersed within a cloud, or dripped upon from above under a overhanging canopy.
I have used a fine mist sprayer on a timer, which I alter periodically to prevent regularity. Works a treat.
They will take exposure and lower temperatures providing they are rained upon. Even in the tropics they withstand high UV levels but with regular descending cloud bases.
For me, that's the trick when moving - ensure they are rained upon, one way or the other.

Tree ferns roots are basically the trunk, hence why they can be bought as just a trunk and are shipped over as a basic log!
The do put very fibrous black roots down into the soil, but the main important area is the crown where they mainly feed and trunk.
But as big root ball is always good!
Water the base and top, as normally you wouldnt worry about the trunks base, but as its been disturbs, it would be best.

Thanks for the advice. Sounds like it is worth the risk of moving it.

It was very happy at first, but the canopy above it has got so dense it is now very dry and doesn't get the rain at all. (Very interested in your advice about a mist sprayer, Burgundy. Thanks) Although I water and feed well, I have noticed over the last couple of years that the leaves are getting much smaller. Hope the move suits it.