Yes, you can transplant asparagus. It can be tricky, particularly with anything like mature plants, because of the complexity of the root structure that will have developed. It's a bit like trying to unravel knots. Best done early in Spring, while they're still dormant. It took me a couple of goes to wangle out the roots without murdering too many of them.
hi italophile sorry for long time reply ,
been up in the air with move regards Ian
Just let them grow freely as the ferny stems are photosynthesising and feeding the roots - the more ferns the better. Cut the stems down to about 5cm after they die in the autumn. What you shouldn't do is start harvesting the young shoots in the first two springs after planting as you want the roots to establish and grow as much as possible.