Can I say this?

[belly_ttt]

The fed let Swagger off the hook after their arriving /arrival to the Department of Justice

 

[Gёггч]

Both are ok,i think.
The former one is more formal ,isnt it?

 

[Anglika]

The fed let Swagger off the hook after their arriving /arrival to the Department of Justice

The Fed(s) let Swagger off the hook after they arrived at the Department of Justice

It is not clear from the sentence if there is more than one federal officer. Maybe more context would help.

 

[belly_ttt]

I thought FBI is the only one?

 

[louhevly]

I thought FBI is the only one?

"the Fed" generally refers to the Federal Reserve Board, an American financial institution. When referring to the FBI, we say "FBI". The agents of the FBI are popularly knows as "feds" (no initial capital letter).

So: The fed(s) let Swagger off the hook after they arrived at the Department of Justice.