O'Reilly, the chief executive of INM, now owns 26.39% of the company after exercising around £3m worth of share options to acquire 2.7m shares.
INM was surprised back in January when it was revealed that O'Brien had built up a 3% stake in the company. He had bought 22.6m shares for an outlay of £40m since November.
The two men have a history of business rivalry, which developed into bad blood.
Five years ago, they were on opposing sides in the takeover of Irish telecommunications company Eircom, with O'Reilly winning the day.
In 2003, O'Brien complained in an interview with The Irish Times that O'Reilly's newspapers had made "outrageous allegations against me and my companies".
O'Brien, who owns a Caribbean mobile telecommunications business called Digicel and stakes in radio stations in Dublin and Europe, has refused to comment on his reasons for buying into INM.
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