Moodle offers Instructors the ability to mark-up or annotate a pdf submitted by a student. No downloading and uploading is required. Changes are saved and visible by the student when she logs in to view her grade.
1) Turn editing On> Add an Activity>Assignment
Submission types > check File submissions
Feedback types > check Feedback comments and check Feedback files
Save and Return to Course
2) View/Grade all submissions
Click on the assignment name.
Click on View/grade all submissions.
In the Grade column for the student you are grading, scroll over to select the little Pencil shape in the Grade category.
Scroll down until you see 'Launch PDF Editor' under Feedback Comments.
Once annotations are complete, close the PDF Editor by clicking the X in the upper right hand corner.
Make any desired feedback comments and grade updates.
Click Save changes or Save and show next to save changes to the PDF and grading screen.
3) To view annotations, Students go into view Grades
Scroll to desired assignment, click on that item, scroll to Feedback and click to view annotated PDF.
'Assignment settings in Moode' https://docs.moodle.org/26/en/Assignment_settings
Youtube: Annotating pdf's in Moodle http://youtu.be/MgsA-9qMBdY