Yes. This is a deep aspect that not many people even notice.
The best way to explain this is as follows:
1. Alobha, adosa, and amoha are sobhana cetasika (. That means they are “good cetasika.”
2. However, “lobha, dosa, and moha can be present INDIRECTLY” as long as one has not comprehended Tilakkhana, i.e., the fruitlessness/dangers in the rebirth process.
– Therefore, a moral person who has not comprehended Tilakkhana, when they generate alobha/adosa/amoha would still have lobha/dosa/moha ‘on the side, not directly.” (P.S. We could say they are there as anusaya, not coming to the surface)
3. In other words, when someone not comprehending Tilakkhana does a deed with alobha, say, there is still some lobha “hidden in there.”
– That level of avijja is eliminated ONLY after comprehending Tilakkhana.
4. I have explained this in the post, “Kusala and Akusala Kamma, Puñña and Pāpa Kamma”
– Please read that post carefully. What I explained above is summarized in #7 in that post.
– “(more and more) PUÑÑA kamma will automatically become KUSALA kamma. Kusala kamma are better than puñña kamma.” That happens gradually as one’s level of understanding of Tilakkhana increases.
5. This is why alobha, adosa, and amoha are labeled as sobhana cetasika, and NOT kusala cetasika.
– In the same way, there are kusala/akusala citta and there is no explicit term as “punnabhi citta.”
P.S. There are, of course, “punnabhi sankhara.” Those are included in sankhara that arise due to avijja as explained in the post, “Saṅkhāra – What It Really Means“.
– That point is in #6 there.
P.P.S. Those punnabhi sankhara AUTOMATICALLY become “kusala-mula paccaya sankhara” (leading to Nibbana) with comprehension of Tilakkhana. See, “Kusala-Mula Paṭicca Samuppāda”
For everyone, it is a good idea to read and comprehend the three posts referred to above.