Do not use human hair conditioner on a dog. Such products are designed for skin that's a different pH to dog skin and can be irritating. In addition, it often contains colorings and scents which may inflame canine skin.
If your hair is severely damaged, it will not be possible to get a color that requires pre-lightening, such as pink, without risking severe damage and breakage.
You can experience some added benefits from a regular conditioner by leaving it on longer and adding heat. However, a true deep conditioner has richer oils in a higher concentration...
Lather your hair with clarifying shampoo and cover it up with a plastic processing cap. Then, heat it up with a hairdryer for 5-10 minutes, which should help the clarifying...
