Is there a word in logic, or science, that means getting the right conclusion from the wrong set of presumptions? Or alternatively, something is correct, but the explanation of why is incorrect. Is there any term from formal logic or science to describe when this happens?
There is no such word that I'm aware of.
According to the strict sense of conclusion that's used in logic and philosophy, it might even be incorrect to say that you actually came to a conclusion in the first place:
1 a : a reasoned judgment : INFERENCE
// The obvious conclusion is that she was negligent.
1 b : the necessary consequence of two or more propositions taken as premises
especially : the inferred proposition of a syllogism
By this domain-specific definition, if what you state is not the result of a reasoned judgment, nor is it the necessary consequence of what went before, then, in the specific context of logic or philosophy, you cannot claim that your statement is a conclusion. It's simply a statement that happens to be true.
You could use the more common sense of conclusion:
2 : the last part of something
// The team was exhausted at the conclusion of the game.
: such as
a : RESULT, OUTCOME
// The peace talks came to a successful conclusion.
In other words:
I concluded my (erroneous) argument by saying …
I came to the conclusion (of my erroneous argument) that …
But, again, in domain-specific language, using the first sense of the word, it would not be considered a logical or philosophical conclusion in the strict sense of that word.
However, it's likely that unless you are being pedantic, such a distinction would not normally be made.
On a related note, there is such a thing as the argument from fallacy.
Argument from fallacy is the formal fallacy of analyzing an argument and inferring that, since it contains a fallacy, its conclusion must be false. It is also called argument to logic (argumentum ad logicam), the fallacy fallacy, the fallacist's fallacy, and the bad reasons fallacy.
Fallacious arguments can arrive at true conclusions, so this is an informal fallacy of relevance.
Note that this Wikipedia article doesn't make the pedantic distinction I did in terms of the senses of conclusion (where I would say the person arrived at a true statement rather than a, to be precise, logically valid conclusion)—nor would I have expected it to.