To my mind it is a poor paraphrase, because an important distinction can be made. That paraphrase also seems to be in quite some tension with one of the last things the Teacher said:
For a long time, Ānanda, you’ve treated the Realized One with deeds of body, speech, and mind that are loving, beneficial, pleasant, undivided, and limitless. The phrase “undivided and limitless” (advayena appamāṇena) normally describes kasiṇa meditation (AN 10.25:1.3); here it is also found in the Sanskrit: ānanda maitreṇa kāyakarmaṇā hitena sukhenādvayenāpramāṇena. Dīgharattaṁ kho te, ānanda, tathāgato paccupaṭṭhito mettena kāyakammena hitena sukhena advayena appamāṇena, mettena vacīkammena hitena sukhena advayena appamāṇena, mettena manokammena hitena sukhena advayena appamāṇena. You have done good deeds, Ānanda. Devote yourself to meditation, and you will soon be free of defilements.” On the eve of the First Council—in about six months time—Ānanda devoted himself to meditation and achieved arahantship. Katapuññosi tvaṁ, ānanda, padhānamanuyuñja, khippaṁ hohisi anāsavo”ti.
DN 16
Here the Teacher is referring to Ananda as a doer of deeds, “You have done good deeds, Ānanda.” It also says that Ananda achieved the result of those deeds, “Ānanda devoted himself to meditation and achieved arahantship.”
So we cannot find the quote or even a close paraphrase, but we can find the Teacher saying something quite the opposite. Given this I think that quote or paraphrase should not be attributed to Vajira or the Teacher by Buddhagosa.
