Is that using correct?

Hi everyone.

Can we use relative clause in the middle of sentence like this?

—

The prosecutor accused Mr Fuller, former vice-chair of the US National Intelligence Council, of having links to Muslim cleric Fethullah Gulen.

—

There is appereantly no “who is” in that sentence but actually I think, there is invisible “who is” there.

—

The prosecutor accused Mr Fuller, who is former vice-chair of the US National Intelligence Council, of having links to Muslim cleric Fethullah Gulen.

—

Is this using correct? That’s because my teacher said that you couldn’t say:

“I invited a man, who is an engineer, to the party.”

According to him, It would be

“I invited a man to the party, who is an engineer.”

But for the first sentence i give, doing it is difficult.

—

The prosecutor accused Mr Fuller of having links to Muslim cleric Fethullah Gulen, who is former vice-chair of the US National Intelligence Council.

—

I don’t know whether it is true. Who does “who” refer to? Fetullah Gulen or Mr.Fuller?

I think it is referring to Mr.Fuller, because there is a comma.

What do you think about them?