How to pass fields values
First of all: This introduces redundant data into your DB. Generally this isn't a good idea.

If you must for some reason:

You can implement hook_node_presave for content type B. You get the fully populated $node. This gives you the possibility to load the referenced node type A and grab the value you want to set in B.

Maybe you want to consider to implement the same for content type A. This gives you the possibility to propagete this value every time it changes.