Seven-year-old Neon will have radiotherapy treatment, following surgery on a brain tumour, against his mother's wishes.
Specialists treating Neon accepted that there were side-effects to radiotherapy but said that without the treatment the youngster could die within a few months.
Mr Justice Bodey, who heard evidence at a hearing in the Family Division of the High Court in London, said radiotherapy treatment could start.
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The British Muslim convert insisted he is not "currently" a fighter in Syria.
The four people who were all related were killed on the A64 near Malton as they returned from a wedding in Leeds.
Sir Philip Green said he is "sad and sorry for all the BHS people caught up in this horrid story".