I understand that it is preferable to go to the mosque even before Adhaan and it entails huge reward. But the narration says that the angels stop writing down after the Imaam rises on the pulpit and the Adhaan is given. This seems to suggest that there is no reward for persons who come after Adhaan and your answer to one of the previous question also suggest this. Is my understand correct?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The narration you are asking about proves that the person who enters the mosque on Friday after the Imaam has ascended the pulpit does not get the reward of going early to the Friday prayer. Going in the early hours to the Friday prayer has a special reward as mentioned by the Prophet : "Whoever goes to the Friday prayer in the first hour, it is as if he sacrificed a camel. Whoever goes in the second hour, it is as if he sacrificed a cow …. And when the Imaam starts Friday sermon the angels fold up their registers and sit to listen to the sermon." (The time from sunrise until the Imaam ascends the pulpit is divided into five internals the length of which varies depending on when the Imaam does ascend, by arriving during the first segment the person is entitled to the reward of sacrificing a camel). The narration does not negate the reward of attending the sermon and performing prayer. So, the reward of such acts will be recorded as Allaah says (interpretation of meaning): {So whoever does an atom’s weight of good will see it}[99:7].

Therefore, whoever goes to Friday prayer during the early hours gets the reward for that, and whoever goes to the prayer after the Imaam has began the sermon misses such reward, and he will only receive the reward of attending the sermon and performing the prayer.

Allaah knows best.