He committed zina with a woman when she was menstruating; does he have to offer the expiation for having intercourse during menses?

Firstly: 

We praise Allah for having enabled you both to repent and
follow the way of righteousness and guidance. 

With regard to expiation, if what is meant is the expiation
for having intercourse during menses, some of the fuqaha’ are of the view
that the one who has intercourse with his wife when she is menstruating has
to offer expiation, which is one dinar or half a dinar. 

Ibn Qudaamah (may Allah have mercy on him) said: If he has
intercourse with his menstruating wife in the vagina, he is sinning and he
should ask Allah for forgiveness. Concerning the expiation, there are two
reports, one of which says that he has to offer expiation because of the
report narrated by Abu Dawood and al-Nasaa’i with their isnaads from Ibn
‘Abbaas, that the Prophet (blessings and peace of Allah be upon him) said
concerning the one who had intercourse with his wife when she was
menstruating: “Let him give a dinar or half a dinar in charity.” And the
second report says that he does not have to offer any expiation; this is the
view of Maalik, Abu Haneefah and most of the scholars, because the Prophet
(blessings and peace of Allah be upon him) said: “Whoever goes to a
soothsayer and believes what he says, or has intercourse with his wife in
her back passage or when she is menstruating, has disbelieved in that which
was revealed to Muhammad, blessings and peace of Allah be upon him.”
(Narrated by Ibn Maajah.) And he did not mention any expiation. And because
it is a kind of intercourse that is forbidden because of the harm caused, so
it is like intercourse in the back passage. 

And al-Shaafa‘i has two opinions like these two reports. 

End quote from al-Mughni, 1/203 

And they differed concerning the case where that happens in
the event of zina; some of them were of the view that expiation is also
required in this case. 

It says in Mataalib Ooli al-Nuha (1/245):  He has to
offer expiation, whether he had intercourse with a woman in a halaal manner
or by way of zina. So he has to offer expiation of one dinar or half a
dinar. End quote. 

In order to be on the safe side, you should offer the
expiation. One dinar is equivalent to 4.25 grams of gold. And there is a
choice with regard to the expiation: one dinar or half a dinar. 

Secondly: 

We have discussed previously the stipulation of repentance in
order for the marriage contract after zina to be valid, how that repentance
should be done and the ruling in the case where it is not known whether
repentance has taken place. Please see the answer to question no.
131467. 

And Allah knows best.