Reduction from $HALT$ to $A_{TM}$

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: