He prayed in a place, then after the prayer he discovered that there was a cross near that place

The cross is a symbol of the Christians
which they venerate because they believe that the Messiah was killed and
crucified on it. This is a false belief that was declared false by the Holy
Qur’an, which stated that it is a lie and misguidance. Allah, may He be
exalted, says (interpretation of the meaning):

“And because of their saying (in
boast), ‘We killed Messiah ‘Eesa (Jesus), son of Maryam (Mary), the
Messenger of Allah,’ – but they killed him not, nor crucified him, but the
resemblance of ‘Eesa (Jesus) was put over another man (and they killed that
man), and those who differ therein are full of doubts. They have no
(certain) knowledge, they follow nothing but conjecture. For surely; they
killed him not (i.e., ‘Eesa (Jesus), son of Maryam (Mary) )”

[an-Nisa’ 4:157]. 

It was the practice of the Prophet
(blessings and peace of Allah be upon him) – as it says in Saheeh al-Bukhaari
(5952), in a report from ‘Aa’ishah (may Allah be pleased with her) – that he
did not leave anything in his house on which there were crosses, but he
would break it and change it. 

Based on that, it is not permissible for
the Muslims to have crosses on anything in their houses, furnishings or
mosques. 

It says in Fataawa al-Lajnah ad-Daa’imah,
in fatwa no. 7810: 

The cross is a symbol of the Christians
who put it in their places of worship and venerate it; they regard it as a
symbol of their false belief, which is the crucifixion of the Messiah ‘Eesa
ibn Maryam (Jesus son of Mary – peace be upon him). Allah, may He be
exalted, stated that the Jews and Christians were lying about that, as He,
may He be glorified and exalted, says (interpretation of the meaning):
“but they killed him not, nor crucified him” [an-Nisa’ 4:157]. So it is
not permissible for Muslims to put crosses on the furnishings in their
mosques or elsewhere, or to leave them there; rather they must get rid of
them blotting them out and erasing their features, so as to avoid evil and
avoid resembling the Christians in general, and with regard to that which
they regard as holy in particular. End quote. 

But if a person prays facing towards
something on which there is the design of a cross, or in a place where there
is a cross, his prayer is still valid, even though it is makrooh, and he has
to avoid that in the future. 

The scholars of the Standing Committee for
Issuing Fatwas were asked: Can a Muslim pray on a mat on which there is the
design of a cross? 

They replied:

If the question is about the ruling on a
prayer that was done on a mat on which there is a cross, the prayer is
valid, in sha Allah, although it is makrooh. 

However, if the question is about the
ruling on doing that in the future, then he must remove the cross from the
mat, by erasing in in such a way that will remove its features, or by
placing a fixed cloth over it, or by replacing this mat with one on which
there is no cross, because it is narrated in a saheeh report from ‘Aa’ishah
(may Allah be pleased with her) that the Prophet (blessings and peace of
Allah be upon him) would not leave anything on which there were crosses but
he would cut it out. 

End quote from Fataawa al-Lajnah ad-Daa’imah
(3309) 

The scholars of the Committee were also
asked: 

What do you say about watches on which
there is a cross? Is it permissible for us to pray wearing them or not? 

They replied: 

It is not permissible to wear the watches
on which there is a cross, either when praying or otherwise, unless the
cross is removed by scratching it off or covering it up. But if a person
prays wearing it, his prayer is still valid. 

What he must do is hasten to remove the
cross, because it is one of the symbols of the Christians, and it is not
permissible for a Muslim to resemble them.

End quote from Fataawa al-Lajnah ad-Daa’imah,
question no 9 in fatwa no. 2615 

The ruling mentioned above, that it is
makrooh, only applies to the one who is aware of its presence. If it was the
case that he was not aware of the cross being there until after he had
finished his prayer, then there is no sin on him and it was not makrooh in
his case, and his prayer is valid, in sha Allah. 

And Allah knows best.