Shouldn't it be "See you on Monday." instead?

1

Before leaving, the woman also told her superior, “See you on Monday”.

Shouldn’t it be “See you on Monday.” instead? If not, why is it so?

Thanks.

2

You are correct.

See you on Monday.
This is an incomplete sentence (sentence fragment).

Sentence fragments usually require an upper case letter at the start, and a period at the end.

This is also a quotation. As a quotation at the end of the sentence, the period belongs inside the quotation mark.

3

Thanks, NearNapping! Sorry for the belated thanks!