Conversation so far:
Did they have any clues?
probably FSB) are known to have targeted the webmail account of the murdered Russian journalist Anna Politkovskaya.
How did they target her email?
On 5 December 2005, RFIS initiated an attack against the account annapolitovskaya@US Provider1, by deploying malicious software.
Did they get into trouble for that?
CANNOTANSWER.
Did they have any murder suspects?
After the three Makhmudov brothers, Khadjikurbanov and Lom-Ali Gaitukayev were convicted in 2014.
Did they go to jail?
CANNOTANSWER.
Is there anything else interesting in the article?
In accordance with Russian law there is a 15-year statute of limitation for the "particularly grave" crime of first degree murder.

Question: Are they close to solving it?
Self-contained rewrite: Is FSB close to solving the murder of Anna Politkovskaya?