How long after marrying a citizen and becoming a citizen can that person remarry an illegal alien?

The issue of divorce may in fact be irrelevant.

The USCIS/ICE is no longer recognizing all marriages between unlawfully present foreign nationals and US citizens as valid.

When the foreign national applies for citizenship Immigration officials will do an in depth investigation as to the legality of the marriage.

If it is found that the union took place for the sole purpose of the foreign national to gain permanent residency or citizenship, both parties can be charged with a federal felony.

The penalty to all involved parties for being convicted of entering into a fraudulent marriage is a maximum of 5 years in a federal facility and a $250,000 fine. The convicted illegal immigrant will be deported to his or her country of origin and permanently barred from reentry into the US. The US citizen will have a permanent criminal record of having commited a felony offense.

That aside, naturalized citizenship can be revoked (denaturalized) at any time for many reasons including the divorce of a citizen spouse, therefore a time limit does not really matter.