I don't think it's a matter of an intelligence being strong or weak. I'm relatively confident that the inverse problem of computing the structure of a human brain given a rough history of the activities of the human as input is so woefully underconstrained and nonunique as to be impossible. If you're familiar with inversion in general, you can look at countless examples where robust Bayesian models fail to yield anything but the grossest approximations even with rich multivariate data to match.

Unless you're conjecturing FAI powers so advanced that the modern understanding of information theory doesn't apply, or unless I'm missing the point entirely.

I think those possibilities are unlikely. /shrugs