[smarx007]

> how do I tell my graph database that the result of the construct query

I am assuming you are asking how to do a CONSTRUCT query that will return you the contents of a given named graph?

https://www.w3.org/TR/sparql11-http-rdf-update/#http-get is a much simpler way to get a graph. As the spec says, it's equivalent to the following query

       CONSTRUCT { ?s ?p ?o } WHERE { GRAPH <graph_uri> { ?s ?p ?o } }