Rather than proteins or any molecular mechanism that hard code memories or information in the brain, neural signaling is a dynamic process that occurs as electrical signals that propagate on partly-static infrastructure. If you could 1) scan the brain in enough detail to see every individual connection between neurons and which of the various signaling mechanisms they have, and 2) read out the electrical activity of every neuron at a snap shot in time, then you'd likely be able to simulate the whole thing.
Learning and memory formation, one the other hand, are slower processes that involve growing or removing connections between neurons and changing the strength with which they communicate with each other. This would make it more difficult to write the simulated brain back into the living brain: you'd have to update the physical structure of the neurons, including what connections they have and the density of neurotransmitters/receivers in the cell membranes between them. Now, the brain obviously has the mechanisms to make these changes (these "learning" mechanisms are much less understood today than the signaling itself) but it wouldn't natively happen as fast as your simulation. A possible "plausible" explanation is some genetic manipulation that fast-forwards the biological brain to the final simulated brain state, quickly and efficiently bypassing the many slow "real-time" iterations the simulated brain had to go through while you were learning your lessons.
As an aside, there are a couple confusing comments/answers that put too much weight on the idea of information being stored in proteins or other molecular mechanisms of computation. So, here's a short primer that should help get the feel of how we understand neurons to work:
Communication between neurons, and the way they represent information and do computations, is done with electrical signals. The most basic unit of neural information is the action potential: a brief, all-or-nothing, zero or one, voltage change across the neuron's cell membrane. This signal can be further communicated to other neurons, causing them to fire their own discrete action potential. While the details are unknown, the neural signalling all takes place in the strength, frequency, and timing of connections of huge populations of neurons communicating with each other one binary (more or less) bit at a time. The way these connections are developed over time represent all sorts of comparators and integrators and memory circuits and other higher-level logical units that consist of many neurons firing 0/1 with complex connections between them. Fundamentally it is a dynamic process, and neurons don't hold information for very long, nor do they store proteins or some other kind of "hard-disk" storage. The molecular basis of the action potential is based on the movement of ions across the cell membrane in a positive-feedback loop. This is initiated by neurotransmitters sent from the axon terminals of one neuron to the dendrites of another neuron. The configuration of neurotransmitters and receivers in the gap between neurons can hard-code the strength of the signal communicated from one to the other. This and the presence of a connection in the first place are the building blocks of the neural circuit that represents information by firing action potentials around. Think of it like a dynamic digital logic block. It proscribes specific input/output relationships and by putting many of them together you can design the output.
