We have a migration project, where we need to transfer the document library's content of various Alfresco (4.0 CE) sites to the document library of related Liferay (6.2 EE) sites.
1) The simple approach would be to copy on WebDAV file share layer all documents from left to right. Would that work?
2) Is there a way to keep the document's history as well? Do we need to use some API for that or is tooling available within the products?
There is no native migration path between Alfresco and Liferay.
Transferring all documents using WebDAV would certainly work as Alfresco supports WebDAV and Liferay can bulk import using WebDAV but you should be aware that this will not bring across any of the metadata associated with those documents/folders. You may have to look in to ETL to get everything.
Your only likely full solution would revolve around exporting all of the files from Alfresco as an ACP (Alfresco Content Package) which is effectively a zip or by using the Alfresco Bulk Export Tool. This will export all documents and their metadata but bear in mind you still won't get the versions doing this, for that you may have to query against the version store directly.
The problem then seems to be with Liferay as it has no bulk insert mechanism. There is someone in a thread here that has had the same issue and the only solution is to use Liferay's Document Library API.
So in summary, if the users are happy not having all metadata then I would go ahead and use WebDAV, it's going to save you a lot of heartache.