"speaking" is a verb like "running" is a verb... Do you say - "This is her running." LOL! If you do.. my question to you is... Is it YOUR running?

On the other hand

"speech" is a noun as "ball" is a noun... so you say, "This is her ball." You would ask... "Is this her ball?" you don't ask "Is this she ball?"

The point here is, "THIS IS SHE" is the correct term.

THIS IS SHE is the correct terminology. To those who seek to find the right term, it would be "This is she." How funny one person actually thought "speaking" was a noun when used in the sentence "This is her speaking." LOL! -- it is a verb, dork! Speaking is a verb in this sentence. Another example would be this: This is her ball. You can say that, but not -- This is she ball. In this sentence "ball" is a noun so it is appropriate to say "her" however speaking (which is the topic of this forum - to answer a phone call, what the appropriate answer would be?) is a verb therefore This is she speaking is the correct sentence. don't get confused nor be fooled with poorly formed language or as you call it "slang" words. It is THIS IS SHE!