Is this abduction an "Affirming the Consequent" fallacy?

There are three different issues here.

First, the form is invalid.  It violates the fallacy of Categorical Logic called the Fallacy of Undistributed Middle.   The term "Distributed" means that a statement must be true about every member of the class.  In at least one premise the middle term must be distributed for the argument to be valid.  The Middle term is the term that appears in both premises, in this case "mortal".   It is not distributed in either premise and thus commits this fallacy.

As to the two meanings of the word "man", that's the fallacy of Equivocation--where a term with two different meanings is used in the same argument in two different ways.

Finally, the issue here is whether the argument is deductively valid.  The term "abduction" refers to something else--where one forms a conclusion based on the best evidence available at the time.  That's not what's going on. here.

Yes it indeed is. If you accept that all people who are humans are mortal, then saying, "If all matter that is human is mortal, then everything that is mortal means it is human" though the conclusion may sound correct, the way used to get to that conclusion is immensely incongruent and needs to be looked at because obviously, there are things that are not human and are still mortal, for instance birds.

Back to the original question about Abduction and Affirming the Consequent, Abduction is the process of assuming something is true because it is the simplest explanation of something that’s observed.  So if X’s fingerprints are found on the murder weapon, the detective can “abduce” that X may have been the killer.  In that sense, abduction is a type of “affirming the consequent”:

If X used the gun to commit the crime, X’s fingerprints would be on the murder weapon.

X’s fingerprints were on the murder weapon.

Therefore X used the gun to commit the crime.

—

Initially, it should be noted that unlike deductive reasoning, the claim is not that the conclusion must follow from the premises, but only that it is a "valid" hypothesis.*  In everyday life we use such reasoning all the time (we see something and we assume that whatever was the most straightforward cause did in fact cause it).  But it’s a hypothesis, not a certainty.    

BTW: It seems unintuitive to apply abduction to an abstract argument such as All men are mortal / Socrates etc.

—

*As Cristian points out, it is deductively invalid to say:

If P then Q.  Q   Therefore P.    In deductive logic that is the Fallacy of Affirming the Consequent.

Cristian, don't worry about the language thing.  It's difficult mastering a new language (English, in your case) without also having to master the language of Logic (for all of us on this site).

As you say, there is a standard logical form, but it isn't the form you mentioned.

It's more like:  If P, then Q;  P;  therefore, Q (note the different placement of the second Q and P).

Consider: If it's a lion, it roars; Fluffy is a lion; therefore Fluffy roars.  If we use P for "is a lion" and Q for "it roars", then the argument would look like:  If P, then Q;  P;  therefore, Q.  (If it's true that all lions roar and that Fluffy is a lion, then Fluffy must roar – a valid conclusion.)

If we were to use the logical form you presented [If P then Q; Q; therefore P], we'd have an argument like:

If it's a lion, it roars; Fluffy roars; therefore Fluffy is a lion.  Here the logical form breaks down and the conclusion doesn't follow logically from the premises ... perhaps Fluffy is a bear, a male ostrich, an elephant, an ape, or some other animal with an appropriately shaped larynx, hyoid bone, and internal space for air – they all roar, too.

You mentioned abduction in your question.  Abduction can be considered a process coming up with a collection of explanations  (as opposed to a single explanation) for an observation (in your example, mortality).  Your observations seem to point to Socrates being mortal, but for the process of abduction abduction to be complete, we would need to see if there are other explanations, like perhaps things other than man being mortal.  If evidence shows other things being mortal as well, then Socrates might be one of those other mortal things, as you suggest in your examples.  (Of course, for this particular issue, it depends on how one defines "mortal".)