If you change material properties for a particular material that is used by multiple projects, then those material property changes will automatically be available to all groups in those projects. Therefore the associativity between materials and groups will be maintained. However, in order to see those changes, you will need to "Analyze" each of those projects. Before you analyze these projects, the results shown will reflect the results from the last analysis performed (which used the previous material properties).
There is a tool available to users that are signed in as "HyperSizer Admin" that can be used to determine which projects and groups are using which materials. The tool is called the "Material Cleanup" tool.
On the main HyperSizer menu, go to Tools | Material Cleanup. You will get a listing of all of the materials in the database. Some of the materials will have a (P) indicating it is used by at least one project or an (L) indicating it is used by at least one laminate. If the material is used by a project, select the material and press the "Report" button. You will see a listing of all laminates and projects that use this material. If you select one of the listed projects, you will get a listing of which groups in that project use that material. If you see "(Project References Material Only)", this indicates that the material was made available in the Project Available materials form, however it is not being used by any group.
Please let me know if you need more information.