A is the correct choice and below is my understanding of why that is .
First , for comparisons - 'LIKE' should be followed by noun entities and 'AS' should be followed by a clause .
The given statement can be properly written in two ways :
1. A fact that only few are aware of is that like Marie Curie, her daughter Irene Joliot-Curie was awarded the Nobel Prize.
2. A fact that only few are aware of is that Irene Joliot-Curie was awarded the Nobel Prize as her mother Marie Curie was.
understood as
A fact that only few are aware of is that Irene Joliot-Curie was awarded the Nobel Prize as her mother Marie Curie was (awarded the Nobel Prize).
In 1 , Marie Curie is compared with her mother . Like is only followed by a noun and the point of comparison is getting awarded the Nobel Prize.
In 2, the comparison is between the action of getting awarded. And so, AS is used.
Note that ellipsis is in play here as the verb can be omitted and still the meaning will not change. For that, omitted words should
already exist somewhere
BEFORE in the clause. This is the reason by B is incorrect.
Hope it's clear now.