I know the reduction to from $ A_{TM}$ to $ HALT$ . But is the following reduction **from** $ HALT$ to $ A_{TM}$ correct?

We are looking for total computable function $ f$ mapping from $ HALT$ to $ A_{TM}$ . The following TM $ F$ calculates the reduction $ f$ .

`F = on input <T, w> create the following TM T': T' = on input v: start T on v if T accepts or rejects, *accept* return <T',w> `

I think the line `if T accepts or rejects, *accept*`

is correct, but it would be great if someone could check this.

Edit: I found the following slides, but I don’t think the construction in there is correct: http://slideplayer.com/slide/13791105/