What is the ruling of Islamic law on helping a girl who claims to be transferring a large sum of money from her account to my private account, with a promise of receiving a percentage of the money in return? And is this money considered permissible?

It is unlikely that a girl would not find someone trustworthy to safeguard her money in her own country, or that she would place complete trust in someone she has never met. Scholars have reached a consensus on the prohibition of a woman traveling without a mahram if there is fear of fitna (temptation/strife). They differed, however, if suspicion is remote; some of them maintained the prohibition based on hadiths such as, "It is not permissible for a woman who believes in Allah and the Last Day to travel for a day and a night’s journey unless she is accompanied by a mahram." A woman gifting some of her money to a man is permissible and commendable if it is free from corrupt intentions, unless the gift is a means to disobey Allah. Accordingly, the aforementioned girl's travel to the questioner's country without a mahram is impermissible.