Your child would likely be eligible to extend their PBS dependent visa provided they are "not leading an independent life" AND you got your visa based on a PBS route and not on the Long Residence route. How did you get your ILR?
Interpretation wrote: “Must not be leading an independent life” or “is not leading an independent life” means that the person:
(a) does not have a partner; and
(b) is living with their parent (except where they are at boarding school, college or university as part of their full-time education); and
(c) is not in full-time employment (unless aged 18 or over); and
(d) is wholly or mainly dependent upon their parent for financial support (unless aged 18 or over); and
(e) is wholly or mainly dependent upon their parent for emotional support.
So you would want to show that your child was at uni and probably also that he returns regularly to the UK for his holidays, to spend time with his family outside term time.
Keep in mind that his long absences from the UK will have impact on things other than his immigration status. Home Student status and student finance in England requires that they have been resident in the UK and Islands for the full three year period before the first day of the first academic year of the course AND also either have at least ILR or have resided in the UK for at least half their life (so, at least 9+ years). So, your child will have to pay the Overseas Student rates for their Masters degree, even if they are living in the UK. (As an aside, that was the case with me too. When in the UK on my Tier 1 visa, I had to pay the Overseas Student fees for my part-time Masters that I was doing alongside my full time job. So I was paying full taxes in the UK, but was billed as an Overseas Student.).
Also keep in mind that your child will need to meet the full absences requirements for British citizenship in his own right as an adult. So the long absences now will considerably delay his British citizenship.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.
