Is he who fasts six days of Shawwal after Ramadan, while also making up ten days that he missed in Ramadan due to a legitimate Shar'i excuse, rewarded as if he had fasted for an entire lifetime?

The estimation of the reward for deeds is for Allah alone, and the servant who seeks recompense from Allah will not have his reward lost. Whoever broke their fast in Ramadan must first make up for what they missed, and then fast six days of Shawwal to achieve the virtue of following the Ramadan fast with six days of Shawwal.