This is a really good point actually.
Say Mum passed in August 2023, granny passed in January 2024. Half-brother hadn't spoken to step-mum for a considerable number of years.
Between August 2023 and January 2024, half-brother will have learned he's to inherit nothing from his step-mum. He will have had time to think about this.
His half-sister's granny passes away in January this year, and half-sister tells him she's inherited from her granny (her recently deceased mum's mum). Grandmother is no relation whatsoever to half-brother. She will have been a presence merely via his step-mum who helped raised him but to whom he hadn't spoken in many years.
Bear in mind, he's already banked the full inheritance from his own mum.
At THIS point, after he's been dwelling on having received nothing from his step-mum, brother says to half-sister "oh, half of what your grandmother actually belongs to me because your mum said she'd give me half".
It takes a certain type of person to have their eye on someone else's fortune and misfortunes, and turn them to their own benefit.
He's a chancer, OP. He's chancing his arm at other people's money.