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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
What you described as an introduction of marriage may mean engagement which is the mutual consent [between the two parties] to be married to one another while the woman remains a non-Mahram to the man who proposed to marry her until a valid Islamic marriage contract is conducted between him and her, which is the contract that fulfills some conditions, the most important of which are the (consent and presence of the) guardian and the presence of two witnesses. For more benefit, please refer to Fatwa 83629.
If such a contract is conducted, then the woman becomes a wife of that man and he is permitted to do with her what a husband is usually permitted to do with his wife.
As regards the Mahr (dowry), the jurists stated that it becomes due upon concluding the contract, and the woman or her guardian has no right to ask for it before that. In addition to this, the Mahr is the sole right of the wife, and after the marriage she has the right to renounce it in principle, let alone giving respite to her husband for not paying the amount of Mahr that is due immediately, as long as she is adult and of a sound mind.
Therefore, we warn you against considering the Mahr as a reason for dispute especially that the matter is at the beginning, and it might be that even the engagement would not be concluded, not to mention the Islamic marriage contract.
Finally, it should be mentioned that your sister should cut any relationship with that man before the marriage contract as he is a non-Mahram to her and it is not permissible for a woman to have an affectionate relationship with a non-Mahram man outside marriage. For more benefit, please refer to Fatwa 81356.
Allaah Knows best.