Does "and further to study" sound natural in English?

goal / is / to identify and to study

what do you want the word "further" to mean?

Context:

The long-term goal of this project is to identify projection-specific biomarker for VTA dopamine neurons and further to study behavioral responses to stress by

The long-term goal of this project is to identify projection-specific biomarker for VTA dopamine neurons and further to study behavioral responses to stress by...

I thought of that, and then rejected it because the comma changes the meaning subtly.
But it's helpful nevertheless.

According to me, further means the any action happen from the current situation.

The difference between the first and second sentences is how the word "further" is being used.

In the first sentence, the word "further" can be read as "what's more," or "additionally."

In the second it seems to mean "to study more in depth."

I think the second phrase could be better put by splitting the infinitive "to study" and inserting the adjective "further:" "and to further study," if that's the sense that you are trying to convey.

P.S. I'm sure JTT is just tickled that you've described his suggestion as " golden Standard English"!

Too late now, I'll come back to this tomorrow, God willing and if'n the creek don't rise.

It's an attempt at a "folksy" expression from America, meaning "if circumstances don't prevent me from doing it".
If a creek rises, if a stream becomes swollen with rain, the road may become blocked.