Silver Lake officially submitted its offer document for Software AG on Wednesday, almost a month after announcing a €2.4 billion (US$2.64 billion) takeover bid.
The financial investor said that shareholders of the Darmstadt-based group could tender their shares at a price of €32 by June 14.
In its offer document, Silver Lake reiterated that it intends to delist Software AG as soon as practically possible after the transaction.
It has secured 30.1 per cent of the share capital through a binding agreement with company founder Peter Schnell's Software AG Foundation, a charitable foundation and longstanding anchor shareholder, and through purchases on the stock exchange.
However, a non-binding counteroffer from Rocket Software, which belongs to private equity firm Bain, plans to put up to €36 per share on the table.
Software AG's management and supervisory boards support Silver Lake despite Bain's higher offer, drawing criticism from minority shareholders at the company's annual general meeting on Wednesday.
Software AG's chairman of the board of directors, Silver Lake partner Christian Lucas, was absent from the AGM which was run by an external lawyer.
This is very uncommon for shareholder meetings in Germany.
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