All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible for a woman to marry before her elder sister as there is no evidence that prohibits this.
‘Ali Ibn Abu Taalib narrated that the Prophet said to him: “O 'Ali, there are three things which you should not delay: the prayer when its time is due, the funeral when it is ready, and marrying off an unmarried woman when there is a suitable match for her.” [At-Tirmithi, Ibn Maajah, with a chain of narrators that is differed upon among the scholars; however, some scholars classified it as Hasan (good).]
On the other hand, it is an obligation on the elder sister to cut her relationship with that young man, as it is not permissible for a Muslim woman to have an affectionate relationship with a non-Mahram man and the fact that he wants to marry her does not make such relation permissible. For more benefit, please refer to Fatwa 81356.
If he wants to marry her in the future, he should undertake the proper means, which is to ask her hand from her guardian.
Allaah Knows best.