Is purchasing a gift (a golden necklace) for a friend, by having one of the partners pay the full amount and the other settle his share later, considered usury (riba)?

It is clear from the question that the questioner appointed his friend to purchase the necklace, and what the friend paid from the questioner's share is a loan from him to the questioner. As long as the friend bought the necklace from the seller and gave him its full price at the time of the contract, there is no forbidden usury in that.