One mitzvah perfected contains all 613

בהעלותך פרש"י שתהא שלהבת עולה מאלי'.

"Beha'aloscha" (when you kindle) — Rashi explains that the flame should rise up on its own.

The Kohen must kindle the menorah until the flame ascends by itself; the language of "going up" hints that the goal is a fire that becomes self-sustaining.

והרמז עפ"י מ"ש נר מצוה ואיתא רצה הקב"ה לזכות את ישראל הרבה להם תורה ומצות.

And the hint is based on the verse "a mitzvah is a lamp," and it is taught that Hashem wished to give merit to Israel, so He gave them an abundance of Torah and mitzvos.

Connecting "ner mitzvah" (Mishlei 6:23) to the Mishnah (Makkos 3:16) that Hashem multiplied Torah and mitzvos to grant Bnei Yisrael merit, the Sefas Emes reads the menorah's lamp as an image of the mitzvah.

כי הנשמה חלק אלוה ממעל.

For the neshamah is a portion of the Divine from above.

Every Jew's soul is literally a "piece" of the Divine, a spark of holiness from on high.

אבל הגוף מסתיר הארת הנשמה.

But the body conceals the illumination of the neshamah.

The physical body acts as a covering that hides and obstructs the soul's natural radiance.

והמצות מזככין החומר ולהכין דרך שתוכל הנשמה להאיר.

And the mitzvos refine the physical matter and prepare a path so that the neshamah can shine.

Performing mitzvos purifies the coarse material of the body, clearing the way for the soul's light to break through.

לכן נק' נר שהיא כלי והכנה לקבל האור.

Therefore the mitzvah is called "ner" (lamp), for it is a vessel and a preparation to receive the light.

A lamp is not the light itself but the vessel that holds and enables it; so too a mitzvah is the means that allows the soul's light to be revealed.

כמו כן תרי"ג מצות עצות איך שתוכל שלהבת הנשמה להאיר בהאדם.

So too the 613 mitzvos are counsels for how the flame of the neshamah can shine within a person.

The full system of 613 mitzvos is, in effect, Divine advice on how to let the soul's flame illuminate one's entire being.

והרמב"ם בפירוש המשנה כתב כשמקיים אדם מצוה אחת בשלימות זוכה לעוה"ב ולכן הרבה מצות שימצא עכ"פ מצוה א' לכל איש ישראל ע"ש.

And the Rambam wrote in his commentary to the Mishnah that when a person fulfills a single mitzvah in completeness, he merits Olam Haba; therefore He gave many mitzvos, so that at least one mitzvah should be found for every Jew.

The Rambam teaches that even one mitzvah done with true perfection earns a share in the World to Come; the abundance of mitzvos ensures every individual can find at least one he can fulfill perfectly.

ודבריו אמת שבכל מצוה תלוין תרי"ג מצות שכשנתקן אבר אחד כראוי ואז שלהבת הנשמה עולה באמצעיות מצוה זו ממילא מאירין כל האברים.

And his words are true, for within every single mitzvah all 613 mitzvos are bound up; for when one limb is rectified properly, and the flame of the neshamah then rises through that mitzvah, automatically all the limbs become illuminated.

Each mitzvah contains all the others in potential. Rectifying even one limb through one mitzvah perfectly performed causes the soul's flame to ascend, and its light then spreads to illuminate the whole person.

וז"ש בתורה באבותינו הראשונים ויעשו ככל אשר צוה ה' את משה באיזה מצות פרטיות כמו בפסח בפרשה זו ובשאר מקומות.

And this is what the Torah says of our early forefathers, "and they did according to all that Hashem commanded Moshe," regarding some particular mitzvos, such as the Pesach offering in this parashah and in other places.

The Torah praises figures for doing "all that Hashem commanded" even when they actually fulfilled only one specific mitzvah, such as the korban Pesach.

והפי' ע"י שקיימו המצוה בשלימות עשו בזה ככל אשר צוה ה' בחי' תרי"ג מצות התלוין בה כנ"ל:

And the explanation is that by fulfilling the one mitzvah in completeness, they thereby accomplished "all that Hashem commanded" — the aspect of all 613 mitzvos that are bound up within it, as above.

Because all 613 mitzvos are contained within each one, fulfilling a single mitzvah perfectly is reckoned as having kept the entire Torah — which is why Scripture credits them with doing "all that Hashem commanded."

Summary: The Sefas Emes reads the kindling of the menorah ("until the flame rises by itself") as a metaphor for the soul. The neshamah is a portion of the Divine, but the body conceals its light; mitzvos are the "lamp," the vessel that refines the body and lets the soul's flame shine. Drawing on the Rambam, he teaches that each mitzvah contains all 613, so that fulfilling even one mitzvah in completeness rectifies the whole person and is reckoned as keeping the entire Torah — which is why the forefathers who kept a single mitzvah perfectly are credited with doing "all that Hashem commanded."