There is a significant list of examples in Paul's letters where we see him explicitly reporting on Jesus's ethical teachings.
• 1 Corinthians 13:4-7 — “Love is patient, love is kind and is not jealous; love does not brag and is not arrogant, does not act unbecomingly; it does not seek its own, is not provoked, does not take into account a wrong suffered, does not rejoice in unrighteousness, but rejoices with the truth; bears all things, believes all things, hopes all things, endures all things.”
• Galatians 5:22-23 — “But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law.”
Paul expects early Christian readers of his letters to remember how Jesus lived (presumably from having already been taught it in some detail).
• James Dunn: “But typos in Paul’s letters almost always has a personal reference — a particular individual (or individuals) providing a pattern of conduct.” [Dunn here cites, Rom. 5.14; Phil. 3.17; I Thess. 1.7; 2 Thess. 3.9; also I Tim. 4.12; Tit. 2.7; 1 Pet. 5.3; Ignatius. Magn. 6.2; otherwise only 1 Cor 10.6.] “And talk of converts being handed over to the typos makes better sense both of the reference was to a person (cf. Phil. 3.17; 2 Thess. 3.9) and if the person was Christ (the handing over to the new Lord named in baptism). The clear implication is that the information provided regarding Jesus’ conduct and the character of his mission gave new converts a pattern for their own conduct.” [Beginning from Jerusalem, 104.]