The phrase "and on completing" is correct and usable in written English.
It can be used to indicate an action that occurs after finishing a task or process.
Example: "The report will be submitted by Friday, and on completing it, I will send you a summary."
Alternatives: "upon completion" or "after finishing".
Indeed, Joyce said that the ideal reader of the Wake would suffer from "ideal insomnia" and, on completing the book, would turn to page one and start again, and so on in an endless cycle of reading.
He studied graphic design in high school but wasn't much of a student, and on completing his studies he needed a job.
I passed quiet children and quieter fishermen (everyone here seemed to be serene); sat on a rock and watched trout jumping; and on completing the circle, stretched out lazily in the sun.
At its Katanga mines in the Democratic Republic of Congo, where it took over management control in 2009, it said, "more than $11m has been spent on reinforcing more than 1,900m of mine shaft roof and on completing mined-out production chamber support, following a thorough review of rock mechanics to improve safety".
And on completing your doctorate, "move on".
Users were mainly focused on the interaction and on completing the puzzle-style task and saw it as a battle between them and the other teams that had completed the task previously with a better time.
Therefore, choose one or two items at most, and focus on completing those.
Google ended 2011 spending $1.9 billion (including cash and stock) on completing 79 acquisitions during the entirety of the year.
They receive a Diploma in Modern and Holistic Medicine on completing their training.
The university requires students to sign a declaration in exams and on completed assignments, stating that they have not breached the rules regarding academic integrity.
Meanwhile, protesters have welcomed Hall and Mills with open arms, and congratulated them on completing a long but rewarding journey.
