You can use the toolboxToolbox for the spatial join (processing toolboxProcessing Toolbox > search: join by locationJoin by Location) and save the result to a temporary layer. The temporary layer is only saved in your QGIS project. Then you can join the temporary layer to the layer A'layer A'.
You can find the processing toolbox in view > panels > toolboxView > Panels > Toolbox
or right click-click over the toolbars.