From a VAT perspective, the sale of shares can be an exempt supply, however as you have pointed out in your email, the question is whether A is providing advice or intermediation or both. Principally, whichever element is the predominant service will indicate whether VAT is due or not.
My guess is the M&A company is VAT registered and A is also VAT registered, and hence both entities maybe VAT neutral even if VAT is charged.