The following might be his source (translations are my own). The gemara in Bava Basra (1ob) says:
ושמעתי שהיו אומרים אשרי מי שבא לכאן ותלמודו בידו
And I heard that they said, "praiseworthy is one who comes here with
his studies in his hand."
And the Maharsha comments:
שהיו אומרים אשרי שבא לכאן ותלמודו בידו כו'. יש לפרש כי עיקר הלימוד
ושנעשה בו רושם הוא הלימוד הבא מכתיבת יד אשר על כן נקראו החכמים סופרים:
One could explain that the essential form of Torah study and that
which make the greatest impression is the study that comes from
writing, as for this reason the Chachomim are refered to as scribes.
That was the main answer, the following is related but probably not what you're looking for. I heard R' Michel Shurkin use this Maharsha to answer up a question that the poskim deal with in the beginning of O"C. In siman 47 sif 3 the Shulchan Aruch says that one must recite birchas hatorah before writing divrei torah. The Taz over there (s"k 2) is very bothered by this and he says that in order to make the bracha and have it not be a bracha levatala the person should be careful to speak a little bit in Torah before he writes (he actually does say that because we say יברכך ה' וישמרך וכו that there might not be an issue, ע"ש). This is in rejection of the suggestion that because when someone writes they usually speak a little bit, that justifies making the bracha (like the Talmid R' Yonah and the Chayei Adam want to say). All of this the Mishna Berura sums up neatly, ע"ש ס"ק ד.
Rabbi Shurkin said in the name of R' Akiva Eiger (teshuvos, mahadura kama siman 29) that "ksiva k'dibur dami" (That's how Rabbi Shurkin said it). He then explained that according to the aforementioned Maharsha R' Akiva Eiger should really have said that "dibur k'ksia dami".
The lashon of R' Akiva Eiger (translation is my own) over there is:
משום דמצות עשה של ת"ת נפקא מקרא דושננתם לבניך...ולמדתם את בניכם מש"ה
ממעטים הרהור, דבהרהור לא שייך ללמד את בניו, משא"כ בכתיבה עדיף בזה
מהרהור, דע"י כתיבה יכול ללמד לאחרים והוא בכלל ושננתם לבניך
...because the positive commandment of Torah study is derived from the
verse, "teach them thoroughly to your children...teach them to your
children." For this reason we eliminate thought, because through
thought it is not possible to teach you children. But this is not so with writing which
is better than though in this regard, because though writing one is
able to teach others, and this constitutes "teach them thoroughly to
your children."
Rabbi Shurkin then said that R' Moshe Feinstein (of whom R' Shurkin was a close talmid for close to 30 years) would always encourage him and others to write as much as possible.
(P.S. It seems that only from the Maharsha do we see clearly that the main beneficiary of writing down what you learn is the one learning/writing. R' Akiva Eiger doesn't necessarily disagree with this, but he does say that in order to constitute talmud Torah, it must be teachable, meaning there must be the possibility of another beneficiary other than one's self, which writing always will accomplish even if while learning you were only thinking in you own head without speaking.)
