Is it permissible to provide a free, permanent internet line to a cousin without the knowledge of the partners, in consideration of his efforts and to avoid their requesting additional lines for their households, which would affect internet speed?

It is not permissible for a woman to open a separate account for her paternal cousin without the knowledge of her partners, as this constitutes betrayal and an infringement upon their rights. Partners must be informed, for a partner only acts within permissible limits. Anything beyond that requires the consent and knowledge of the other partner, as the Prophet, peace and blessings be upon him, said: "Indeed, Allah says: 'I am the third of two partners as long as one of them does not betray his companion. If he betrays him, I depart from between them.'"