For instance, those who live in the world a thousand years from to-day, will read of those who are living now in this great day, and will have great honour for them. They have connection with us by a spiritual union, and they will think of us who have been in the days of this Manifestation. This is a proof of the infinite superiority of the spiritual over the material union. Look at the solidity of the spiritual union. For instance, we think of Abraham and his followers, and we rejoice as we speak of their good qualities, although so many hundreds of years have passed since their time.
(‘Abdu’l-Bahá, Bahá’í Prayers 9, p. 43)

Furthermore, Shoghi Effendi appears to suggest that awareness of the Cause in the next world evolves and unfolds. For example, the following extract from a letter dated 17 March 1940 written on behalf of the Guardian to a believer whose father had recently passed away, provides the following statement: The Guardian ... wishes me to hasten to convey to you the expression of his deepest sympathy in this grievous loss which you have come to sustain. He will specially and earnestly pray for his departed soul that in the realms of the spirit beyond it may receive such guidance as would enable it to fully recognize and accept the Faith, and thereby attain abiding peace and happiness.
(The Universal House of Justice, 1991 Aug 28, The Condition of non-Bahá’í Relatives after Death)

In reference to your questions about ancestors and descendants, we have been directed to say that while there are Tablets from Bahá’u’lláh stating that faith in the Manifestation of God on the part of a believer attracts God’s mercy to the souls of the departed parents the House of Justice knows of no text in Bahá’í Writings to support the statement that a believer’s seven past generations and seven generations to descend from him are blessed when that person becomes a Bahá’í.
(The Universal House of Justice, 1991 Aug 28, The Condition of non-Bahá’í Relatives after Death)

In this regard, it is interesting to note the response, written on behalf of the Guardian, to a believer who asked Shoghi Effendi about (apparently) the same Tablet referred to by Mr. ....and who expressed concern about the spiritual condition of his uncle who had met ‘Abdu’l-Bahá, but failed to accept the Faith. The Guardian’s secretary wrote:
With reference to Bahá’u’lláh’s Tablet in which He says that all the relatives of believers will reach the Kingdom in the other world: by this is meant only a partial attainment. They can, however, progress indefinitely, as spiritual progress in the other World is limitless, and is not confined to those who have attained unto the knowledge and recognition of the Cause while still in this world.
(The Universal House of Justice, 1991 Aug 28, The Condition of non-Bahá’í Relatives after Death)

It is permitted to ask for advancement, forgiveness, mercy, beneficence, and blessings for a man after his death... Therefore children ... must implore pardon and forgiveness for their parents.” (‘Abdu’l-Bahá, Some answered Questions, p 268-269)

One of the distinguishing characteristics of this most great Dispensation is that the kin of such as have recognized and embraced the truth of this Revelation and have, in the glory of His name, the Sovereign Lord, quaffed the choice, sealed wine from the chalice of the love of the one true God, will, upon their death, if they are outwardly non-believers, be graciously invested with divine forgiveness and partake of the ocean of His Mercy. This bounty, however, will be vouchsafed only to such souls as have inflicted no harm upon Him Who is the Sovereign Truth nor upon His loved ones. Thus hath it been ordained by Him Who is the Lord of the Throne on High and the Ruler of this world and of the world to come.
(Bahá’u’lláh, The Compilation of Compilations vol. I, p. 386)

Thou hast mentioned the station of parents in the next world. One of the special bounties of this Revelation is that whoever accepteth the Dayspring of the Cause, his parents, although they may not have attained the recognition of the Revelation, the splendours of the Sun of divine favor will be vouchsafed unto them. This is one of His bounties bestowed upon His lovers. Render thanks and be of those who are grateful.
(The Universal House of Justice, 1991 Aug 28, The Condition of non-Bahá’í Relatives after Death)

While Bahá’u’lláh clearly affirms that these souls are “invested with divine forgiveness", “partake of the ocean of His mercy” and are the recipients of “the splendours of the Sun of Divine favor", the Research Department has not, however been able to locate any statement in the Writings to suggest that one’s non-Bahá’í parents, upon their death, automatically become Bahá’ís.
(The Universal House of Justice, 1991 Aug 28, The Condition of non-Bahá’í Relatives after Death)