Yes moving it is fine, in fact it's a very good idea.
Things to look out for though, avoid routing your pipework over your exhaust manifold for less heatsoak. And try to keep the pipes as short as possible, especially important on a ZE where the intercooler is post-throttle.
The factory one works fine up to a point, but if your mate hammers it constantly of track races it then a bigger/better IC might be a wise move.