He sent a hadeeth in order to spread good, then he found out that it is a fabricated hadeeth. What should he do?

Spreading da’wah messages and letters which contain
explanations of shar’i rulings, or preaching and beneficial stories, is an
important means of doing good, because many people receive them, and it is
easy to send them. But we should make sure that the content is sound and
that the ahaadeeth contained in it are saheeh (sound), because some people
are abusing this great blessing (of easy communication) and are spreading
fabricated ahaadeeth and false stories. 

It is not permissible for anyone to say, “The Messenger of
Allaah (peace and blessings of Allaah be upon him) said…” when he knows
that the hadeeth is mawdoo’ (fabricated) or false. The Prophet (peace
and blessings of Allaah be upon him) said: “Whoever tells lies about me
deliberately, let him take his place in Hell.” Narrated by al-Bukhaari,
1291; Muslim, 933. 

And he (peace and blessings of Allaah be upon him) said:
“Whoever narrated a hadeeth from me which he thinks is false, then he is one
of the liars.” Narrated by Muslim in the Introduction to his Saheeh. 

Al-Nawawi (may Allaah have mercy on him) said in Sharh
Muslim (1/71): 

It is haraam to narrate a fabricated hadeeth for one who
knows that it is fabricated or who thinks it most likely that it is
fabricated. Whoever narrates a hadeeth which he knows or thinks it most
likely to be fabricated, and does not explain that it is fabricated, is
included in this warning and is included among those who tell lies about the
Messenger of Allaah (peace and blessings of Allaah be upon him). This
is also indicated by the hadeeth quoted above: “Whoever narrated a hadeeth
from me which he thinks is false, then he is one of the liars.” Hence the
scholars said that the one who wants to narrate or quote a hadeeth must
check it. If it is saheeh or hasan, then he may say, “The Messenger of
Allaah (peace and blessings of Allaah be upon him) said such and such,
or did such and such, etc”, expressing certainty. If it is da’eef (weak),
then he should not say, “he said” or “he did” or “he commanded” or “he
forbade” and other such definitive words, rather he should say, “Such and
such was narrated from him” etc, or “it was narrated” or “it was said” or
“we heard that” and so on. And Allaah, may He be glorified, knows best. End
quote. 

He also said: 

With regard to the prohibition on telling lies about the
Prophet (peace and blessings of Allaah be upon him), no distinction is
made between reports which contain rulings and those which do not contain
rulings, such as preaching and exhortation, etc. In all cases it is haraam
and is a major sin and abhorrent action, according to the consensus of the
Muslims whose consensus counts, unlike the innovators who falsely claim that
it is permissible for fabricate ahaadeeth of exhortation, and who are
followed in that by many of the ignorant who claim to be ascetics. End
quote. 

With regard to what you have done by spreading this
fabricated hadeeth, the expiation for that is to ask Allaah for forgiveness
and to strive to inform everyone to whom you think you most likely sent this
hadeeth that the hadeeth is fabricated. And Allaah burdens not a person
beyond his scope [al-Baqarah 2:286]. 

You should not spread any hadeeth after this until you make
sure that they are soundly attributed to the Messenger of Allaah (peace
and blessings of Allaah be upon him). 

And Allaah knows best.