Use a simple filter.
On the table B, create a compo filter based on A (FK). Drag a sub field of the FK node. (To display text values in the combo)
Then, you can call this page in various ways.
- The user set the filter value
- The link of the page specify it (...&filter_myfk=33)
- The menu item set it automatically (In the menu item setup)
- a small PHP code filter the model : $model->setState('filter.myfilter', 33)
There are many ways...
Also you can group the grid B depending of the FK value