Playing on ExtHD

So recently my laptop kicked the bucket, but luckily the pc repair place recovered my hard drive and put it into an external enclosure so I could keep using it. Since LoL was already installed on it, , is it just a matter of plugging it into another computer and playing like normal or is there something more complicated involved? I've never owned an external drive before, so I'm unfamiliar with how they operate. Thanks for any help!