On page 130 of The Queen's Diamonds Roberts confirms that another notable Teck jewel, the Duchess of Teck's flower brooch, was in Queen Mary's possession by 1923.
Roberts states that this brooch was given to George VI, then Duke of York, for QEQM when they married.
As we know Roberts does not give any dates for when Queen Mary acquired her mother's crescent tiara or the hoop necklace, but I think it is reasonable to assume that she acquired all the jewels from her brother at one time.
As the Royal Collection dates the acquisition of the bracelet as 1919, it is possible that Queen Mary purchased all the jewels then.