The phrase "recently wrapped up" is correct and usable in written English.
It can be used to indicate that a particular event has recently been completed. For example: The team recently wrapped up their project and are now looking to their next endeavor.
I recently wrapped up a 33-city book tour.
Newtown High School recently wrapped up a $41 million renovation, adding a wing with culinary arts facilities.
The group recently wrapped up a UK tour and have only one more date scheduled, 19 November in Osaka.
The announcement comes after The Wolverine, starring Australian actor Hugh Jackman, recently wrapped up filming in Sydney.
His organization recently wrapped up its second year of a European edition, with offshoots planned for Latin America and Asia.
It's an unusual cable extension of a broadcaster's show, and it affirms the popularity of "Glee," which recently wrapped up its first season.
O'Neill spent almost 10 years at Google in various roles, recently wrapping up a stint heading up global business operations inside of Google [X].
The show's first three seasons aired on Lifetime, with the third season recently wrapping up just a few months ago, in April.
Just 23 years old, Horn has a number of credits to her name, recently wrapping up "Violet & Daisy" with James Gandolfini.
I am a sucker for a solid speech, and with graduation ceremonies just recently wrapping up around the U.S., I've spent a lot of time listening to and reading commencement speeches.
"I first heard him in the '60s, at a show with Aretha Franklin and Dr. John, and I thought then, 'Who IS this guy?' " said 72-year-old blues-folk great Taj Mahal, another Morrison fan who caught Sunday's show after recently wrapping up his own European tour in Paris.
