Which is correct: "when you have finished" or "when you will finish"?

Solution 1:

When you have finished to move the furniture, let me know

This is simply wrong. English speakers would not use the infinitive here, but the gerund form of the verb: "When you have finished moving the furniture, let me know."

When you will finish moving the furniture, let me know

This has a strange sound to it. I suppose you could use a somewhat less strange-sounding version of this, perhaps "Let me know when you will finish moving the furniture," implying that you expect the addressee to complete that action and are wondering about his intentions in that regard. It also implies that you are interested in the time the process will get under way. It is not grammatically incorrect to reverse the order of the request, as you have in your example, but it just sounds odd.

In short, both constructions sound as if they originate from a non-native speaker.

Solution 2:

In normal English (i.e. aside from legalese) we hardly ever use an explicitly future tense ("will", "shall", "will have") with a subordinating conjunction such as "if", "when", or "after" (but not, I think, "although");

There are some apparent exceptions with "if", such as

"If he will go, I'll go with him",

which has a slightly different meaning from

"If he goes, I'll go with him"

but I actually think that this is only formally a future, and really uses the auxiliary in an older sense, meaning "If he is willing to go", so it is actually present tense. (For me it implies that he may be unwilling to go, and the statement is an offer, whereas the second is simply a neutral statement of intent.)

But I can't think of an exception with "when".