Isn't it right to say "stepmother", not "step-mum"?
There are different ways to refer to family members. Just as "Mom" and "Mum" are used as casual, shortened forms of "Mother," "Step-mum" (or "Stepmum") is also used as a more casual form of "Stepmother." Ex: My stepmother helped raise me, so I basically consider her to be my real mother. Ex: In my family, I have a mother, stepfather, and two step siblings.
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