iPhone 4s on iOS 6.1.3 not updating

So, a bit of context.

I found my old iPhone 4s and I want to be able to use it in case anything goes wrong with my current iPhone, problem is it’s on iOS 6.1.3, one thing I know is on older iOS versions (below iOs 8.4.1) you will be offered 8.4.1 on A5 devices (which includes the iPhone 4s). I’ve downgraded iPhone 4s devices before by tricking the iPhone into thinking it’s on 6.1.3 when it’s on 9.3.5. When I try to update this iPhone it will infinitely check updates

iOS 6.1.3 in about page

My 30 pin cable won’t sync so I cannot update via iTunes and then downgrade to 8.4.1. Does anyone know how to fix this?