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Explanation: This is the usual phrase here in the US, and you will find it well-attested by searching this phrase in any engine.
I would not worry to much about the subtle difference between "offering" shares and "placing" them. The shares are offered for sale and then are placed (bought) at the price the market deems appropriate.
Alan Lambson Local time: 00:47 Native speaker of: English PRO pts in pair: 114
49 mins confidence: peer agreement (net): +1
place shares on the market
Explanation: note you cannot say <stocks>, which would mean shares of more than one company, rather than more than one share of a single company.
20 years in the business - most of it managing translation service for an investment bank