From a Jain standpoint, your comparison is clear, but the Buddhist rebuttal still does not answer the Jain claim about the jīva. Jainism holds that the soul is a real, enduring, conscious substance; karma is subtle bondage attached to that jīva; and mokṣa is the liberation of that same jīva from all karmic bondage. ( jainknowledge.com)

So the core Jain reply is:

• Memory: Jainism accepts continuity because the same jīva persists through time.
• Karma: Jain ethics is grounded in a real bearer of karmic bondage, namely the jīva.
• Responsibility: moral accountability belongs to the same living soul that acts and later experiences results.
• Liberation: mokṣa is not merely the ending of craving; it is the soul’s complete freedom from karma. ( jainknowledge.com)

On your Buddhist reference check: AN 6.63 is indeed a real Aṅguttara Nikāya discourse often cited in Buddhist discussions of karma; the exact wording is commonly used in that context, though the precise quotation should be verified in the edition you are using. ( thebuddhaswords.net)

If you want the shortest Jain counterpoint in one line, it is this:

Buddhism explains continuity without a self; Jainism says continuity itself presupposes a real jīva, and without that jīva, karma, bondage, and mokṣa lose their true basis.