Subsidiary's own recognised intangible asset affecting goodwill?

The intangible assets 60,000 in the individual financial statements of Beta represent goodwill which arose on acquisition of an unincorporated business in 2008. No impairment of this goodwill has been necessary since the date of acquisition of Beta by Alpha.
Note: Alpha is the parent, controlling 80% of Beta (subsidiary)

Question: Must the intangible asset recognised in Subsi be adjusted and deducted from FV of NA on date of acquisition to calculate goodwill?
I know any individual company is not supposed to recognise any internally generated goodwill/intg asset, but this arose from another acquisition, no?