This will require a little setup. Trust me that this is for a good cause.
The Background
A friend of mine has run a non-profit public interest website for two years. The site is designed to counteract misinformation about a certain public person. Of course, over the last two years those of us who support what he is doing have relentlessly linked to the site in order to boost it in Google so that it appears very highly when you search for this public person’s name. (In fact it is the #2 result, right below the public person’s own site). He does not have the support of this public person, but what he is doing is in the public interest and good.
The friend had a stroke recently. Coincidentally, the domain name came up for renewal right when he was in the hospital and his wife missed the email about it. A domain squatter snapped up the domain, and put up content diametrically opposed to his intent. This squatter is now benefitting from his Google placement and page rank.
Fortunately there were other domains he owned which were aliased to point to this domain, i.e. they used a DNS mapping or HTTP 301 redirect (I’m not sure which) to send people to the right site. We reconfigured one of the alias domains to point directly to the original content.
We have publicized this new name for the site and the community has now created thousands of links to the new domain, and is fixing all the old links. We can see from the cache that Google has in fact crawled the original site at the new address, and has re-crawled the imposter site.
The Problem
Even though Google has crawled both sites, you can’t get the site to appear in relevant searches under the new URL!
It appears to me that Google remembers the old redirect between the two names (probably because someone linked to the new domain back when it was an alias). It is treating the two sites as if they are the same site in all results. The results for the site name, and using the ‘link:’ operator to find sites that link to this site, are entirely consistent with Google being convinced they are the same site.
Keep in mind that we do not have control of the content of the old domain, and we do not have the cooperation of the person that these sites relate to.
How can we convince the Googlebot that domain ‘a’ and domain ‘b’ are now two different sites and should be treated as such in results?
EDIT: Forward was probably DNS, not HTTP based.
Google will detect the decrease in links to the old domain and that will hurt it.
Include some new interesting content on the new domain. This will encourage Google to crawl this domain.
The 301 redirects will be forgotten, in time. Perhaps several months. Note that they redirected one set of URLs to another set, not from one domain to another. Get some links to some new pages within the site, not just the homepage, as these URLs will not be in the old redirected set.
Set up Google Webmaster Tools and submit an XML sitemap. Thoroughly check everything in Webmaster Tools about once per week.
Good luck.