Been looking at youtube, and I see some examples from the cartoon to which you are referring. No actual Beatles covers, but some very Beatlish tunes just the same. If imitation is the sincerest form of flattery....To Firepoint: As for the Beagles, there actually was an album and singles by a studio group by that name; connected with the soundtrack of a Saturday morning cartoon show, "The Beagles," which was the last series made by Total Television Productions (the Underdog folks.) It aired on CBS and the records came out on Columbia. They did not cover "We Can Work It Out" or any other actual Beatles songs as far as I know though, so the record your pal had was something else.
I came across footage of a Mexican group performing some Beatles tunes under the name the Beagles. The clip that I listened to actually wasn't half bad, but the sound quality wasn't all that great, either. It was someone capturing a live performance, probably on a camcorder. I was not able to view it in high enough resolution, but it appeared that they had taken a Beatles banner, and had crudely made the "T" into a "G." At any rate, the footage appeared to be much too recent to have been anything from the '60s or '70s.