Hi ALANDJUDY, the best time to move/plant your Rhubarb is early spring or end of summer befor or after any frost if you get any in your area, this is because the Rhubarb will be in it's domant stage, once you dig up the clumps (they have tough roots and are deep) you will be best to devide the roots into more managable clumps, but not too small, then dig a very large planting hole, really deep also, add lots of animal manure with some soil into the hole, then the Rhubarb clump, backfill with the same soil mix and give a real good water, this will help the soil to get into the root system and also help the plant, Rhubarb is a very thirsty plant and need a real rich soil to recover and give you the nice thick strong stalks that you want, it may not stalk up too well the first year you do this, but will next and after.
Do be careful when you break up the plant that you dont damage the growing tip, it looks like a big red blister, but it is firm, this is what sends out the stalks and leaves, you will need to use your spade to chop this into bits as it is like tree trunks in texture, maybe a sharp bread knife will help. but make the cuts clean through. some people say dont pick the stalks first year, as you want the plant to really bulk up, but as yours is a well established plant, I dont think that will be a problem for you, in Scotland we make Rhubarb and ginger jam for winter and it sure warms you up. good luck. WeeNel.