Thank you for your question, Karin.  Whether a transplant of a Mahonia is successful depends upon its size, using the correct method, and maintaining it through the first year after the move.  I don't know what "sizable" means, nor whether you have an upright variety, or a "creeping" (spreading) type.

In either case, what you observe above ground is probably the same size as the root system--both vertically and horizontally.  Since the upright variety can reach 6-8 feet, getting the entire root ball out can be a challenging endeavor.  Once you get it out, keeping it moist continuously, the hole in which it is transplanted into needs to be the same depth as the ball, and twice as wide.  It, too, needs to be kept moist until it is filled, replacing the native soil in around it, and watering again.  Do not walk on this soil.

Early spring or late fall are generally the best times to transplant woody plants.  If done now, you will need to monitor it during the upcoming hot, dry months, to make sure the soil doesn't dry out.  An inexpensive soil water meter can help you know when to water.  This is especially important if its new residence is in full sun, or primarily sun in the afternoon.  This Extension article indicates that they prefer shade and protection from winter sun and wind.  https://woodyplants.cals.cornell.edu/plant/print/150

I hope this is helpful.   Good luck.