I hope you're doing well!
As I'm nearing graduation and starting to pursue job opportunities, I working to bolster my LinkedIn profile to catch the attention of recruiters. Would you mind writing a quick recommendation on my profile based on the ________ (specific group project, research job/duties, etc.) that we worked on together in the next two weeks? I certainly enjoyed working with (or for?) you and grew professionally through the experience.
I'd be happy to reciprocate with a similar recommendation on your profile if you'd like. Alternatively, if you would prefer, I can draft something for you to adapt and post on my page instead.
Thank you in advance,
Here is a similar letter I sent to colleagues when I left my job at GE Healthcare:
Good Afternoon _______,
As my time on the PET team draws to a close, I have begun to put my affairs in order in preparation for the next chapter. Not knowing what exactly is in store for the future, I am updating my resume and jotting down notes about my experiences in PET for potential opportunities down the road. While it’s still fresh on our minds, would you please post a quick recommendation of me for my LinkedIn profile? … even if your recommendation is for them to “stay far, far away from this candidate.” :)
If you would like, I would be more than happy to reciprocate and share something on your page as well.
It, of course, has been a pleasure working with you over the past few years, and I will remember you and the team very fondly.
As a connection of mine on LinkedIn pointed out, you can boost the likelihood that you will get a response by feeding them a few ideas of what they could recommend when you reach. Otherwise, it could be challenging for the recommender to get started with a blank slate. You want to make it as easy as possible for them without actually writing the review for them.