Just put some Araldite or suchlike in the hole, put that thing in, wiggle it and then let it go off
the screw you show is not a wood screw. It is a machine scew, held in place with a nut or similar object.
so you look inside the wooden thing, and there will be a nut or similar, which you undo with a spanner or other tool
When you find the nut, (or a similar suitable one), push the screw partly in to the hole and then use the slackness, (wobble), to fit the handle back easily.
Once the loop handle is in place tighten up the nut to draw the faceplate back into position. You may need to fit washers inside the drawer under the nuts.
The nut will be an old imperial thread, not a modern metric one. You might have to try a few different thread types to find the right one.
Just put some Araldite or suchlike in the hole, put that thing in, wiggle it and then let it go off
Yes the glue will hold the fixing in place
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