Targuinius persuades the Romans to elect him king

This from Orberg’s adapted Livy (LLPSI).

Tarquinius has given a speech explaining why he should be the next king, recounting his learning of Roman rituals and laws.

Haec eum haud falsa memorantem ingenti consensu populus Romanus regnare iussit.

There is a translation of this in Perseus which goes: "While he was recounting these undoubted facts, the people by a great majority elected him king. "

Is a more literal translation

The people of Rome commanded him, recalling these undoubetly true things, to rule. (?)

What has me confused is haec Given that memorantem is an accusative participle - can a participle retain it’s own object - haec (accusative plural neuter)?

Yes. Participles are the sharing construction – they share in the qualities of both the adjective and the verb. Adjectively, they can modify nouns in number, gender and case, and be used substantively. As verbs, they retain tense (aspect, really) relative to the main verb, and voice. If active, they can take objects…