Colour remover from black

The dandruff shampoo thing is fine, but probably won't make a lot of a difference, if any. I wouldn't bother with the washing up liquid before. Just a clarifying wash with no conditioner and left to dry before you use it. It needs to be as clean as possible. You'll need to leave it to dry between each application too.

It's likely, unless she uses a silicone heavy dye and straighteners, that using the removers will get it plenty light enough for a brown, ginger red. It'll probably be close to that anyway. You don't need it blonde. You might have to bleach bath her roots, but stay away from any permanent dye or bleach until it's a week later. If anything will make it reoxidise it's that.

Clarify her hair before the colour removers and dry it. The hair needs to be as clean as possible first for the remover to work well. You might need to bleach bathe afterwards depending on the result. If her hair does need a bleach bath then wait a week first 🙂

If she has been dyeing it black for a long time you may need more than one round of remover. I have had the best results using a remover, then using fading methods like dandruff shampoo before the second round of remover. My hair is naturally a dark/medium brown and after removing black permanent dye it was a wearable shade of gingery red brown.