Security in case of Malicious and Augmented Semi-Honest Adversaries
As pointed out in the comments, an augmented semi-honest adversary is one who can change its input before the protocol execution begins, but from then on the adversary runs the protocol specification exactly.

Note that if a protocol is secure for malicious adversaries, then the simulator must be able to work also for an adversary who changes its input and then behaves honestly. Thus, the protocol is secure also for augmented semi-honest adversaries.

The reason that this does not work for semi-honest adversaries is because the ideal-world simulator for a semi-honest adversary cannot change the input. That is, in the case of malicious adversaries, both the real adversary and the ideal simulator are stronger than for semi-honest adversaries. This fact means that security for malicious adversaries does not necessarily imply security for semi-honest adversaries (because the ideal simulator cannot run in the semi-honest case if it needs to change the input of the corrupted party). In the book, we give an explicit counter-example of a protocol that is secure for malicious adversaries but not for semi-honest. I know that this is extremely counter-intuitive, but that's the reality.