I have noticed that ALL lines (not braids), even the best nylon lines, have a memory.
Fluoros all have a memory. They have a tendancy when you pull up the knot to form a few twizzly bits near to the knot. But this does not weaken the line as long as you spit on it when you tighten the knot.
For your information, Stren and Seaguar seem less prone to memory. They are lovely lines and all those I have shown then to agree.
But the real advantages of fluoro are three-fold.
1: They are less easy to see under water.
2: Being heavier than nylon they sink quickly and lay on the bottom. As fly leaders, they don't require treating with mud etc to make them sink.
3: PVDF (Polyvinylidene di-fluoride) does not degrade due to untraviolet light or hydrolysation (degredation due to contact with water). In theory you can keep a spool of fluoro indefinitely and it will not weaken.
Beware of poor "PVDF".
If you burn it with a match, it should go out when you take the flame away. If it continues burning, bin it!
There are a lot of cheap and nasty PVDFs around that have given the product a bad name.
Stren is one of the best.