Undue influence requires an element of coercion. It is not sufficient to say that the testator was persuaded to write his Will in a particular way. A good way to think about undue influence is if the testator was asked, he would say “this is not my wish, but I must do it”.
The burden of proof with respect to undue influence is on the party asserting the undue influence, i.e. the person challenging the Will.