I have seen several references where certain gedolei yisroel of yesteryear, promise that if a person learns their works, these Rabbonim will be מליץ יושר (advocate) for them in the olam haemes.
Examples include the following:
Rav Yechezkel Abramsky zt"l about whom it is related:
שנפטר בכ"ד אלול תשל"ו...וציוה שמי שילמוד בספריו יהיה מליץ יושר עליו בעוה"ב
Who died on the 24th Elul 5736 (1976)...and commanded that whoever would study in his books, he would be an advocate for them in the Next World.
[As related in Rivevos Ephraim, Orach Chaim, cheilek beis, p. 248]
"והנה כבר נודע לנשגב את אשר הגיד הגאון לפני פטירתו "שמי שישתדל בהדפסת ספריו יהיה לו למליץ
And behold it is already known what the gaon said before his death - "that one who expends efforts to print his books, he will be to him as an advocate.
ובזה מובן מה שהגיד אדמו"ר זצוקללה"ה קודם פטירתו, שאם ילמדו בספרים שלו יהיה למגן ולעזר גם אחר פטירתו ממש כמו בחיים
And this is understood what the Admor of blessed and holy memory related before his death, that if they learn his seforim he will protect and help even after his death just like in life.
And indeed this is something that the Avnei Nezer reiterated in his own writings - Avnei Nezer, cheilek 5, siman 122, by stating:
ואם היה מעיין בדבריי מעט עיון היה מרויח לו טובה הרבה
And if he studies deeply my words a little, it would benefit him a great deal.
So on to the question....
How can anyone make the claim that they will advocate for a person after they die. Do we have the ability to intercede in the heavenly realms? I appreciate these are great tzaddikim, and perhaps their desire that people learn their seforim is so that they can continue to accrue more zechuyos (merits) in the next world. But is it possible to promise such a thing?