Is it permissible to send a non-transmitted supplication to other women for their use, to make it easier for them, and is there any sin in that?

It is permissible to supplicate with prayers that are not from the authentic traditions, as long as they do not contain a forbidden شرعي (Islamic legal) element. This is based on the Prophet's (peace be upon him) saying: "Then let him choose the supplication most pleasing to him and supplicate with it," and his saying: "The servant's supplication will be answered as long as he does not supplicate for a sin or for the severance of ties of kinship." It is permissible to send this supplication to others, but it is better for each person to supplicate with what they choose without undue effort. The essence of supplication is from the heart, and whoever focuses on rectifying the tongue weakens the heart's inclination. So, one who is in dire need supplicates with their heart, a supplication that opens up to them. Better than all of this, however, is to supplicate with the prayers mentioned in the Qur'an and Sunnah due to their goodness and blessings.