Definite Descriptions

According to Russell, we should translate “The inventor of post it notes is rich.” with the following glossary:

Ix: x \text{ invented Post-it notes}
Rx: x \text{ is rich}

as the following:

\exists{x} (\forall{y}(Iy \iff y = x) \land Rx)

Another way to interpret the sentence is like this with the following glossary:

a: \text{the inventor of Post-it notes}
Rx: x \text{ is rich}

then we get:

Ra

Supposing that both singular terms and russellian descriptions are correct, then my question is whether we can do this?

Ra = \exists{x} (\forall{y}(Iy \iff y = x) \land Rx)

It appears a in the L.H.S is picking out an object in the domain directly while the R.H.S is picking out an object given constrains.