Ah! Thought that there was EU ruling that non registered entities could be in a vat group now. Makes more sense that way alright
There is indeed such a ruling, and the case was actually between Ireland and the EU Commission (and Ireland won)... I suppose I should have been more clear in explaining what it is you misunderstood...!
The VAT group can have exempt or non-taxable persons/entities in it, but remember what the group registration actually means is that the whole group is treated, for the purposes of accounting for CAT as a single accountable person, with supplies between group members (subject to some specific exceptions) being ignored for VAT purposes.
The entitlement to an input credit for VAT is based on the making of taxable supplies, so in a group scenario the VAT on inputs has to be apportioned between the taxable supplies (i.e. those on which VAT is charged, be it at Zero, 9%, 13.5% or 21%) and exempt or non-taxable supplies.
It would help if you could add context to your specific scenario, but taking it at face value, since you say Company A has no customers besides Company B, and if Company B is not actually generating taxable supplies, then a VAT Group comprising only those 2 companies would not be entitled to deduct any input VAT, as the Group (ignoring supplies intra-group) is not making taxable supplies.
I hope that is a bit clearer!