The two extant species of beaver are listed in the genus Castor. Historically this genus had a very wide distribution, in Eurasia ranging from Iberian Peninsula to China and in America from Alaska to northern Mexico.

However, the specimens of Castor from Late Miocene of China exhibit a distinct morphology that falls out of its norms. Therefore, a new genus has been created to list these specimens, called Sinocastor. Some differences between these genera includes: more elongated rostrum and neurocranium with the latter being not as broad, narrow postorbital region, (which are considered to be a more primitive traits) relatively longer incisive foramina and more…

If Sinocastor is a sister to Castor, it would meant that, the common ancestor of these two genera (therefore of a still-living beavers) may come from East Asia. Castor may have dispersed northeastward via Beringian Isthmus to North America and northwestward to Europe.

Here I show my reconstruction of Sinocastor with missing parts filled in by Castor fiber:

Reference:

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0013990