Sariputta and Maha Mogallana (those weren’t their names at the time) go search for the Deathless and learn enough to become Sotappanas. They go in search of the Buddha, presumably he gave them instructions. Then they practiced and were quickly Arahants. Do we have a record of what the Buddha told the pair?
Sāriputta attained arahatta while fanning the Buddha as he taught the Dīghanakhasutta.
Now on that occasion the venerable Sāriputta was standing behind the Blessed One, fanning him. Then he thought: “The Blessed One, indeed, speaks to us of the abandoning of these things through direct knowledge; the Sublime One, indeed, speaks to us of the relinquishing of these things through direct knowledge.” As the venerable Sāriputta considered this, through not clinging his mind was liberated from the taints.
According to the commentaries Mahāmoggallāna attained arahatta on the same day that he was taught the Pacalāyanasutta.
It is an interesting question.
I read the question and the response and amongst other thoughts, ‘can I too wander down that road’. … a bit too simple…. I did some background reading and will back fill and add…
The verses from the vinaya beginning “ye dharmā hetuprabhava” are the words spoken by the Arahant Assaji to Upatissa, later to become known as Sariputta. It is referred to as the Dependent Origination Dhāraṇī. It is suggested that a dhāraṇī is generally understood as a mnemonic which encapsulates the meaning of a section or chapter of a sutra.
“Of those things that arise from a cause,
The Tathāgata has told the cause,
And also what their cessation is:
This is the doctrine of the Great Recluse”
Moggallāna attained arahantship on the seventh day after his ordination, but it was not till a fortnight later that Sāriputta became an arahant. Thus there was a short interval of time spent in the company of the buddha before his nirvana. And from this one assumes there were other instructions leading to the Dīghanakhasutta.
Preceding Sāriputta attainment of arahatta the Buddha said…
“Seeing this, an instructed disciple of the noble ones grows disenchanted with pleasant feeling, disenchanted with painful feeling, disenchanted with neither-pleasant-nor-painful feeling. Disenchanted, he grows dispassionate. From dispassion, he is released. With release, there is the knowledge, ‘Released.’ He discerns, ‘Birth is ended, the holy life fulfilled, the task done. There is nothing further for this world.’ A monk whose mind is thus released does not take sides with anyone, does not dispute with anyone. He words things by means of what is said in the world but without grasping at it.” ~ Dīghanakhasutta
A bit of a neat fit, this Dependent origination and the ultimate nature of feelings ending in disenchantment.
As for me or even you falling in step behind Sariputta, I have been assured it’s only a matter of time and practice…
"In one who keeps focusing on the allure of cling-able phenomena (or phenomena that offer sustenance equals the five aggregates), craving develops. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging and death, sorrow, lamentation, pain, distress, and despair come into play. Such is the origin of this entire mass of suffering and stress.
"Now, in one who keeps focusing on the drawbacks of cling-able phenomena, craving ceases. From the cessation of craving comes the cessation of clinging/sustenance. From the cessation of clinging/sustenance comes the cessation of becoming. From the cessation of becoming comes the cessation of birth. From the cessation of birth, then aging, illness and death, sorrow, lamentation, pain, distress, and despair all cease. Such is the cessation of this entire mass of suffering and stress. ~ Upadana Sutta