How should a merchant in free trade deal with a sum of 150,000 Saudi Riyals that a person wants to invest with him, without making the investor a partner in the capital?

There is no objection to paying money for the purpose of trading with it, provided that the investor receives a widely understood percentage of the profit as agreed upon. This falls under the category of permissible Mudarabah (profit-sharing partnership) if the Sharia-compliant conditions are met.