Can a person sell their portion in olam haba (heaven)? Is the sale valid and binding?
No. The Talmud (מסכת סוטה כ"א עמוד א ) says:
"מאי בוז יבוזו לו? אמר עולא: לא כשמעון אחי עזריה, ולא כר' יוחנן דבי נשיאה, אלא כהלל ושבנא, דכי אתא רב דימי, אמר: הלל ושבנא אחי הוו, הלל עסק בתורה, שבנא עבד עיסקא; לסוף אמר לו: 'תא נערוב וליפלוג!' יצתה בת קול ואמרה אם יתן איש את כל הון ביתו וגו'"
“What does it mean, ‘He will scorn him to the extreme?’ (Shir HaShirim 8:7). Ula says, it is not referring to Shimon the brother of Azariah and Rav Yochanan of the house of the Nasi, but rather it refers to Hillel and Shavna. When Rav Dimi came he explained, ‘Hillel and Shavna were brothers. Hillel delved into Torah and Shavna involved himself with business. At the end [Shavna] said, ‘Let us mix our assets and divide them.6 A Bas Kol shouted out [in response], Should a man give all the wealth of his house for love, he will scorn him to the extreme.”
Translation from Rambam and Zevulun: Boz Yavuzu Lo, by R.A.B. Buchman (PDF). In the article he discusses different views on the Yissachar-Zevulun partnership. Some rishonim say that a man can share the merits of his learning with the person who supports him, but this has to be agreed on beforehand. That way the supporter can get merit for helping someone to learn Torah. But after the learning has been done, there is no way to "sell" the merit, and attempts to do so are deserving of "scorn" (בוז יבוזו לו). The article paraphrases R' Yerucham:
if the chacham actually writes a contract to sell the already learned Torah, he loses the merit he had gained for this Torah learning although the purchaser does not acquire it
If you can't sell merit for one deed, you obviously cannot sell an entire "portion" in olam haba. However, while the sale won't be good, it could help one lose his own portion.
וראה בשו"ת מהרש"ם (חלק ג סימן קנא) שהביא תשובת מהר"ם אלשקר (סימן קא), שהעתיק בענין זה תשובת רב האי גאון, וכתב שם שאין נתפס שום קנין בשכר עולם הבא, כי צדקת הצדיק עליו תהיה, ורשעת הרשע עליו תהיה. ע"ש.
It is not possible (see the above Teshuvot and Sefer WeEn Lamo Michshol vol. 10).
The Maharam Al Ashkar (#101, quoted in R' Akiva Eiger on Shulchan Aruch 246) brings from R' Hai Gaon that it is impossible and forbidden, and one who does risks losing it all.
However, in Rabbinic literature, there are a couple of stories which seem to indicate the validity of such sales.
- There is a famous story of the Vilna Gaon who supposedly paid for an Esrog with it's schar.
- A frightening story is told (brought in the Hakdama to Tochachas Mussar of the Maharsha) about a businessman who sold his Aveira to his partner, who came back to him in a dream summoning him to the heavenly court for a Din Torah about the validity of the sale. The Maharsha summoned the dead partner to his Beis Din, where he paskened that the sale was valid, but the perpetrator (live) was required to do Teshuva and save the purchaser from his fate.
- A third story is told by R' Chaim Volozhen (Ruach Chaim 1:1) of a woman who came to the Taz with a sick child, and the Taz 'donated' the reward of his Talmud Torah to the child.
The שלטי גיבורים in Baba Kama 32b implies that one can sell Schar, for the 10 Zehuvim (gold coins) referenced in Chullin 87. He differentiates between mitzvos one is going to perform to mitzvos one has performed already. (See, however, שו״ת משיב דבר סי׳ י״ד.)
The Gemara in Kiddushin 31b and Sanhedrin 48b bring the concept of הריני כפרת משכבו, which Rashi explains as accepting the punishment for another's misdeeds.
The אמרי בינה (Shu"t §13) makes a distinction between שכר סגולי and שכר גמולי, one which can be sold and one which cannot.
(See also Sefer Chassidim 445, Shu"t Minchas Chaim 2 §20, Shu"t Maharsham 3 §151, Shu"t Btzel Chochma 6 §26, Shu"t Minchas Yitzchok Ch. 7 §88)
I saw a wonderful sefer in a store (Z B Books) in Boro Park. The book was called מכירת עולם הבא" בהלכה". It answers all the questions and thoughts above and also cites many stories of gedolim that help to explain it all. For example, it cites the Maharsham and Reb Shlomo Kluger as saying that you can not sell it.
It's cheap (I think $5); it pays.