And as Dr. Byte and just about all upgraders would say, do one or the other, move your site or upgrade it, but don't do both at the same time.

If you must leave the old site, upload the 1.3.9h version to your new site and get it setup to "minimally" function then move your old site to your new site. Then... Upgrade.

If you still have time and can afford the cost of both sites being "active" then you could upgrade your old site and then move it to your new location, but I would think this riskier. So would go with the first option.