He incited a woman to leave her husband, then he married her and claimed that her son from her first husband was his child

Firstly: 

What this
man did of encouraging the woman to run away from her husband and get
divorced from him by means of khul‘ is a haraam action and a grievous sin.
It is not permissible for a Muslim to propose marriage to any married woman,
or to turn her against her husband, even if that is not with the aim of
marrying her and he has no interest in her, no matter what the reason. A
stern warning concerning that was narrated in the hadeeth of the Prophet
(blessings and peace of Allah be upon him): “He is not one of us who turn a
woman against her husband.” Narrated by Abu Dawood, 2125; classed as saheeh
by al-Albaani in Saheeh Abi Dawood. 

Secondly: 

What the
woman did of getting divorced from her husband by means of khul‘ with no
good reason is also the subject of a stern warning, in the hadeeth in which
the Prophet (blessings and peace of Allah be upon him) said: “Any woman who
asks her husband for a divorce with no good reason, the fragrance of
Paradise will be forbidden to her.”

Narrated
by at-Tirmidhi, 1187; classed as saheeh by al-Albaani in Saheeh Abi
Dawood. 

Thirdly: 

Because of
the crime that they have committed and the abhorrent nature of what they
have done, some of the scholars are of the view that if a man turns a woman
against her husband, it is not permissible for him to marry her; rather it
is permanently forbidden for him to marry her. This is the view of the
Maalikis. However, the majority of scholars think that the marriage is
valid, despite the sinful nature of their actions. 

Fourthly: 

It is not
permissible for this man, or anyone else, to claim the child of another man
as his own; rather this comes under the heading of lies and false
declarations, transgression against the rights of others and corruption of
lineage, and it leads to serious evil consequences. For that reason, Allah
has forbidden adoption (in the sense that the adopted child is claimed as
one’s own flesh and blood) and claiming the child of another as one’s own,
even if the birth parents agree to that or his father is not known. So how
about if he usurped the child and falsely claimed him as his own? This is
even worse and even more abhorrent. 

Allah, may
He be exalted, says (interpretation of the meaning):

“Allah
has not put for any man two hearts inside his body. Neither has He made your
wives whom you declare to be like your mothers backs, your real mothers.
(Az-Zihar is the saying of a husband to his wife, ‘You are to me like the
back of my mother’ i.e., You are unlawful for me to approach.), nor has He
made your adopted sons your real sons. That is but your saying with your
mouths. But Allah says the truth, and He guides to the (Right) Way.

Call
them (adopted sons) by (the names of) their fathers, that is more just with
Allah. But if you know not their fathers (names, call them) your brothers in
faith and Mawaleekum (your freed slaves). And there is no sin on you if you
make a mistake therein, except in regard to what your hearts deliberately
intend. And Allah is Ever Oft-Forgiving, Most Merciful.”

[al-Ahzaab 33:4-5]. 

What they
must do is fear Allah and repent to Him from these sins: his sin of turning
a woman against her husband and her sin of obeying him in that and getting
divorced from him by means of khul‘, then his sin of claiming the child of
another man as his own, and her helping that evildoer in his evil act and
transgression. They should both beware of the wrath and punishment of Allah,
and they should realise that Allah is severe in punishment and that He may
or may not give a respite. Allah, may He be exalted, says (interpretation of
the meaning):

“Consider not that Allah is unaware of that which the Zalimoon (polytheists,
wrong-doers, etc.) do, but He gives them respite up to a Day when the eyes
will stare in horror”

[Ibraaheem 14:42]. 

Muslim
narrated in his Saheeh (2583) that Abu Moosa (may Allah be pleased
with him) said: The Messenger of Allah (blessings and peace of Allah be upon
him) said: “Allah, may He be glorified and exalted, grants respite to the
wrongdoer, but when He seizes him He will not let him off.” Then he recited:
“Such is the Seizure of your Lord when He seizes the (population of)
towns while they are doing wrong. Verily, His Seizure is painful (and)
severe” [Hood 11:102]. 

For more
information, please see questions no. 84849 and
185184 

And Allah
knows best.