I'm not exactly sure how the mathematics would work here but if an electron or any charged particle were in the magnetic grasp of a magnetar and it's electromagnetic field somehow crossed the boundary of its binary Partners Event Horizon would the magnetar's electromagnetic field, electromagnetism being significantly stronger than gravity, be able to retrieve information from Beyond an event horizon? Now, I get the feeling the event horizon would dissolve the electromagnetic bonds; however, is there anywhere in the math that could allow for a black hole with x properties to have information siphoned by a magnetar with y properties?
Statements such as "electromagnetism is much stronger than gravity" have an extremely specialized meaning. In this case the statement refers to the typical magnitude of forces between elementary particles with a charge of a few units of elementary charge and masses comparable to those of usual Standard model particles. However, this comparison of force strengths is irrelevant for the example of the magnetar.
This is because the event horizon is not an instance of gravity being particularly strong. For example, on the horizon of supermassive black holes gravity is weak by any local measurement of the gravitational forces! To see that, you have to compare the space-time curvature. A back-of-the-envelope computation will then show you that a supermassive black hole with the mass of $10^9$ solar masses (and we know of such black holes) has a significantly smaller space-time curvature on its horizon than there is on the surface of the Earth.
So how does one characterize the event horizon? It is best characterized as an accumulated effect. The gravity curves the space-time for so long away from the "flat" state at spatial infinity that suddenly a causality change is possible. And there is really nothing local forces can do about that beyond that point. Drawing information from the black hole is then about as likely as bringing a message about the future. This can also be seen from the math. The direction "inside" at the black hole horizon actually becomes the direction "into the future" for any physical field or matter, including electromagnetic fields.
So no, a magnetar cannot draw information from behind the horizon of a black hole.