Arya Samaj, a religious organization founded by Swami Dhayananda Saraswati (1824-1883) could offer help. This organization offers service for procedural conversion to Hinduism. This conversion practice was originally started by the founder as early as in 1877 to bring back such of those Hindus who had been converted to some other religion by choice or by coercion, who were subsequently willing to come back to Hinduism.
The procedure involves a vedic purification ceremony Called "Shuddhi Karma".
One who wants to convert to Hinduism can approach AryaSamajTemple (existing at several places in India), make a written application along with an affidavit stating that he/she is agreeing for the conversion based on his/her free will, along with proof of age and residence signed by the applicant along with 2 witnesses.
The Shuddhi Karma (purification ceremony) involves conducting a "homam" (a typical Hindu ritual done in front of fire) involving chanting of certain Hymns from the Vedas by the applicant, as guided by a priest. It may take about one to one-and-a-half hours to complete the ceremony. After the purification ceremony, a Certificate of Conversion to Hinduism is issued to the applicant.
It is said that the conversion certificate issued by Arya Samaj is legally valid based on Indian Government Order dated March 19, 1985.
With this certificate in hand, the converted Hindu can marry the Hindu man/woman in Arya SamajTemple as per traditional Hindu marriage rites. For the marriage too, the couple has to give an application with proof of age, place of residence, etc. and an affidavit for consenting for marriage out of free will. The application must be signed and supported by 2/3 witnesses. After completion of marriage ceremony, A certificate of Marriage will be issued by Arya Samaj.
The Marriage certificate from Arya Samaj is a perfect legal document (Arya Samaj Marriage Validation Act, 1937 & Hindu Marriage Act, 1955, Sections 2(a) and subsection (c) of the explanation to Section 2). For the purpose of getting a passport, immigration, Visa. etc. a formal marriage registration with the Registrar Office will be required, which can also be done by submitting the Arya Samaj Marriage Certificate.
A few words of caution:
(1) Though "Indian Government Order dated March 19, 1985" is mentioned above, it is based on other sources at Internet. This author has not personally verified the statement, nor could he locate the specific document's contents or details on this Government Order in other Internet sources. Perhaps it has to be verified outside the web.
(2) In Hindu society, caste system is a practical and sociological reality. Certain castes in Hinduism considered backward get privileged reservation in educational institutions and Government jobs; Arya Samaj Certification will not help in the caste orientation of the converted Hindu.