I have been asked to reattach a kitchen high up wall cupboard that has fallen off the wall

The cupboard was attached to a wall which as far as I can see consists entirely of plasterboard and it was attached at each of the two back corners using plasterboard fixings which have simply pulled out of the wall because of the weight of the cupboard.

I have yet to closely to examine the wall to find out if there are any wooden uprights behind the plasterboard panel, but my initial exploration by tapping the wall seems to suggest that there is absolutely no woodwork anywhere behind the plasterboard in the area in which the cupboard needs to be attached.

I'm going to start off my exploration by drilling lots of small holes across the panel of plasterboard to try and find some solid upright piece of wood behind the plasterboard.

I'd like to support this cupboard using a long strip of wood at the back of the cupboard just under the top edge but my problem is how to attach this to a wall which is so insubstantial.

Irrespective of whether I find any wooden uprights behind the plasterboard I'm thinking that I could screw a large piece of plywood to the wall roughly the same size as the cupboard and at the top of this piece of ply I could attach a strip of wood which will support the cupboard, I am hoping that the plywood would distribute the weight of the cupboard sufficiently to allow the strip of wood to hold the weight of the cupboard.

I would plan to cut a strip out of the back panel of the cupboard with my multi tool to allow the strip of wood on the wall to come into the back of the cupboard just below the top panel then I'd screw the top panel to the piece of wood with some screws going through top panel

I'm wondering what people think of my idea and whether there are any better suggestions

An added complicating factor in the story is that I don't have anybody to help me do this so I need to get something screwed to the wall which will be ready just to receive the cupboard in one go instead of having to mess about holding it up and adjusting etc