The ḥadith was recorded by al-Ṭayālisī: Shuʿbah narrated to us from Muḥārib ibn Dithār who said, “I heard Jābir say …,” and he recounted it.
This chain of transmission is of the highest soundness.
Al-Bukhārī, Muslim, and Aḥmad also brought it through several routes from Shuʿbah.
Musʿar likewise followed Shuʿbah, narrating from Muḥārib something similar; al-Bukhārī and Aḥmad included that version.
Wahb ibn Kaysān also followed him on the authority of Jābir with a comparable report that contains an additional phrase, and Muslim recorded it.

The plain wording of the Prophet’s instruction indicates that performing the two-rakʿah prayer in the mosque upon returning from travel is obligatory, yet I know of no scholar who has actually held this view. If it turns out that someone has, we will adopt it. Allah knows best.

(9) He should step out of the mosque with his left foot first, the reverse of the manner of entering, for this is part of the Sunnah as noted earlier; see the discussion under “Entering the Mosque,” paragraph (5).

(10) When leaving he should say: “Bismi-llāh, Allāhumma ṣalli ʿalā Muḥammad wa sallim, Allāhumma innī asʾaluka min faḍlik” (“In the name of Allah. O Allah, send blessings and peace upon Muhammad. O Allah, I ask You for Your bounty”). At other times he should say: “Allāhumma iʿṣimnī (in one wording: ajirnī; in another: aʿidhnī) min al-shayṭān al-rajīm” (“O Allah, protect me—or: grant me refuge, or: shelter me—from Satan the accursed”). All of this must be said, for the Prophet expressly commanded it, as already noted.