My brother applied for a US visa in 2008 with a fake document and it was refused on those grounds. In 2015, he got the visas of and traveled to two Schengen countries on another passport. He intends to travel to the UK later this year for a week-long conference. Will the previous US visa refusal be an issue since his biometrics were taken then and does he need to declare these in his UK visa application?
Yes, they share information. The controlling reference for this is a treaty between the US and UK which was drafted in 2013 and entered into force last year (2014) which says in part...
CONSIDERING that the effective administration and enforcement of the immigration and nationality laws of the United States of America and the United Kingdom are important to protect the health and safety of their populations, to maintain the security of their societies, and to promote international justice and security by denying access to their territories to persons who are criminals or security risks;
ACKNOWLEDGING that identification of individuals who are inadmissible under their respective immigration laws enhances their ability to facilitate the travel of bona fide visitors;
Source: Agreement between the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of the United States of America for the Sharing of Visa, Immigration, and Nationality Information
So the answer is yes, the two governments share information, not only by this treaty (and similar ones), but also by terms implicit in the "Special Relationship".
The shared data includes biometrics.
Similar question, but framed as 'visa-on-arrival' rather than 'visa-application': Slightly illicit: felon traveling on a US passport; will I be refused entry to the UK?
Based upon all of this, it is natural to conclude that a pejorative history in one of the signatories will affect visa decisions in the other signatory. This does not mean visa applications will be automatically refused, the decision-maker in each country will decide based upon all available information and sometimes this can be favourable to the applicant; but most of the time it would not be favourable to the applicant.
If you take sharing to mean the UK hands over all the data to the US and the UK gets some data on request -- then yes they share.