When the fast of the firstborn falls on a Friday, I read that there is a lenient opinion that one need not fast. I would like to know the source of that opinion.

ב"ה Shalom The Shulchan Aruch (אורח חיים סי' תע)speaks of a situation when the 14th of Nissan falls on Shabbat, then the fast of the firstborn is brought forward to Thursday.The Shulachan Aruch also brings an opinion that holds that in such a case there is no requirement to fast at all. In any case that is not the opinion of the Rema there, but the fast is held on Thursday. However, if the fast of the firstborn falls on a Friday as it did this year(תשע"ה), then the firstborn must fast on Friday, since this is the original date of the fast. פרי חדש ס"ק ב וחוק יעקב סי' תע ס"ק ד' וא"ר סעיף ה שם דרק תענית נדחה אין עושים בערב שבת אבל תענית בזמנה עושים בער"ש) If someone decided to make a personal fast on a Friday then the poskim say that one should not fast on a Friday or at least not fully complete it so that he should not take in Shabbat when he us fasting. ( ריטב"א עירובין מא:, מגן אברהם סי' תע ס"ק ז, משנה ברורה סי' תע ס"ק יח, פסקי תשובות סי' רמ"ט ס"ק ז.) Mo'adim lesimcha