Stephen Thornton describes Popper's position on scientific theories as follows:
As such it [a scientific theory] can be tested and falsified, but never logically verified. Thus Popper stresses that it should not be inferred from the fact that a theory has withstood the most rigorous testing, for however long a period of time, that it has been verified; rather we should recognise that such a theory has received a high measure of corroboration. and may be provisionally retained as the best available theory until it is finally falsified (if indeed it is ever falsified), and/or is superseded by a better theory.
This suggests that scientific theories never reach the status of being verified, let alone true. What one can do with such theories, however, is falsify them.
Douglas Walton describes an argument from ignorance as follows: (page 3)
[David] Kelley ([The art of reasoning,] 148) describes this type of argument as having the form below, where A is a proposition, and the symbol ¬ stands for the negation of A.
¬A has not been proven true.
Therefore, A is true.
This is different from Popper's view of a scientific theory. Popper's scientific theory is never true. The burden of proof remains with those proposing the scientific theory. They, not those opposed to the theory, have the burden to try to falsify the theory.
Consider the question:
In other words: to what extent is Popper's reasoning valid in the context of the Argument from Ignorance and why?
Unlike the argument from ignorance, Popper's theory does not claim that a scientific theory is true, that is, verified. Because of that Popper does not need to rely on an argument from ignorance to verify a scientific theory since a scientific theory is at best corroborated, not verified. The main scientific activity is to look for ways to falsify, not verify, a scientific theory.
Thornton, Stephen, "Karl Popper", The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/fall2018/entries/popper/.
Walton, Douglas, Arguments from Ignorance, The Pennsylvania State University Press, 1996.