Not myself, but I have a similar friend who gets the ability from his photographic memory (interestingly he cannot remember smells and tastes at all!).
Spinoza said, of the three forms of knowledge: sensory, deductive, and intuitive, that only intuitive knowledge is true knowledge. The sense in which I agree with this archaic statement is that I gain knowledge by studying the process and not the details, which is why I can remember a math text much better than a fantasy novel (ironically E.A. Poe critiqued fantasy literature as being analytical in the sense that once the rules of the fantasy realm are established it is a formulaic process to translate our world into the fantasy world according to the rules; where as mathematics is truly creative ).
When reading, strive to create intuitive knowledge. Don't worry about getting every detail, because that is a natural consequence of having an intuitive feel of the process. That said, until one is completely comfortable with the style of mathematical writing, the going is tough. But after this initial barrier, it becomes almost embarassingly easy.
"In mathematics we don't understand things, we just get used to them" - Von Neumann.
What the master meant is that the feeling we call understanding is actually a sensation of familiarity; this is the reason for the uniformity of style across mathematical literature: new definitions in a familiar style are immediately "understandable", with the lucidity being nearly too much to bear.
