The unanimous decision, announced this month, related to Inveresk's sale of its Gemini brand to Scottish paper manufacturer Tullis Russell in 2005.
The latest ruling at the Supreme Court in London revolved around the "additional consideration" that Inveresk alleged Tullis Russell was due to pay in relation to the volume of the Gemini business successfully transferred following the acquisition.
A statement issued by Fife-based Tullis Russell said: "Inveresk has been claiming that a figure of over £900,000 was due and that Tullis Russell was simply dragging its heels unreasonably to avoid this allegedly justified payment.
"Tullis Russell argued that, according to the agreements between the two companies, the amount due should, in its view, be determined by an expert, and be substantially less and be retained pending determination of Tullis Russell's own claim against Inveresk."
Tullis Russell added that this view was "fully and irreversibly upheld" by the Supreme Court's verdict and that its position had been "wholly vindicated".
In a separate issue relating to the Gemini deal, Tullis Russell is suing Inveresk for more than £5m. This action is currently under way in the Scottish courts.
Tullis said this related to the alleged damage to the brand during the handover period in which it claimed that Inveresk had continued to produce Gemini under licence.
The statement by Tullis said: "The dispute also includes a claim for reimbursement of monies already paid out by Tullis Russell in customer complaints on material manufactured by Inveresk."
Inveresk has declined to comment until the conclusion of both cases.