How can I save my Robinia Tree?

It doesn't sound too hopeful, I am afraid. Do a 'scratch' test on the branches you can reach, I mean, scratch off half-an-inch of bark and see if the wood underneath is brown or greenish. If brown and brittle, that branch is dead. Nothing will help the tree if it is far gone. Sorry. You may have to bite the bullet and plant another one for your father.

It is sounding as though your tree is pretty sick.As a desperate measure you could remove the tree to the ground and with a bit of luck allow new leaders to form. After a few years growth, remove all the leaders but leave the strongest. This will hopefully replace the tree in memory of your father yet still remain the tree ( if you know what I mean ). Please research this though as I read of this some years ago and it may well be I'm getting mixed up with something else.Though I'm sure that I'm not, I do not want to be responsible for any premature loss. If I am right ( sure that I am ), there really is no guarantees that this will work.
If you are still getting any suckers/saplings from the mum then is it an option to replace the tree with this ?
Whatever you decide I do hope that you get some positive results.