Off my head I think the Sky has two HDMIs but only one is an output, it does have an Optical out too though.He has a bigger budget than the average person, bear in mind he was budgeting up to £3k for his first projector, and has now bought two in the past week or so.
He was previously considering the top of the range Arcam amps but had some difficulty in connecting them up so I believe they were returned.
Does the projector have 2 HDMI ins? Then one could be run direct to Sky for picture and the other other to the amp for sound.
He might have had a budget of £3K but spent less than half that so he is price conscious which is why I wasn’t going to suggest a £1K AVR which less than half that gets him everything he needs or even less if he sets his limit on surround speaker numbers and whether the Projector was your sole monitor source.
Ideally he needs a new AVR whether a previous gen model or current, if he still has a TV in the room then the small price difference to get dual HDMI outputs would be worth it as you get other benefits.
I must admit that for most people not fully into this hobby the back of a modern AVR is confusing and kind of scaring, my brother is computer savvy but hasn’t a clue about AV gear. I just think he needs a diagram to show him how to connect it all together and everything will be fine though that 12yr old Pioneer Amp has to go.