Gemara

If Shimon is Torem his produce to exempt Reuven's, Shimon has Tovas Hana'ah (he decides which Kohen receives it. A Yisrael may 'bribe' Shimon to give the Terumah to a particular Kohen, e.g. the Yisrael's grandson.)

Nedarim 36b - Question: If Shimon wants to Torem his own produce to exempt Reuven's, does he need Reuven's Da'as (consent or knowledge)?

Since it is advantageous for Reuven, his Da'as is not needed;

Or, perhaps he prefers to do the Mitzvah himself!

Answer (Mishnah): (If a vow forbids Reuven to benefit from Shimon,) he may Torem Terumah and Ma'aser for him with his Da'as ...

Question: What is the case?

Suggestion: Shimon is Torem from Reuven's produce.

Question: Whose Da'as does he need?

Shimon's Da'as is not enough, for he was not made a Shali'ach;

If he has Reuven's Da'as, he benefits Reuven by fulfilling his mission!

(The suggestion is refuted.)

Answer #1: Rather, Shimon is Torem his own produce to exempt Reuven's.

Question: Whose Da'as does he need?

If he has Reuven's Da'as, he benefits Reuven by fulfilling his mission!

Answer: Rather, Shimon's Da'as suffices. This shows that Reuven's Da'as is not needed.

Rejection (and Answer #2): Really, he took the Terumah from Reuven's produce. The case is like Rava said (elsewhere), Reuven said 'whoever wants to Torem may do so.'

Question (R. Yirmeyah): If Shimon is Torem his produce to exempt Reuven's, who has Tovas Hana'ah?

(Shimon has it, for) if not for Shimon's produce, Reuven's produce would be untithed!

Or, perhaps Reuven has it, for if not for Reuven's produce, Shimon's produce would not become Terumah!

Answer #1 (R. Zeira): "Tevu'as Zar'echa v'Nosata" (the owner of the produce exempted gives the Terumah to the Kohen).

Objection (Mishnah): He may Torem for him with his Da'as ...

If Reuven has Tovas Hana'ah, Shimon benefits Reuven (we are thinking that Shimon was Torem from his own produce to exempt Reuven's)!

Rather, Shimon must have Tovas Hana'ah.

Answer: Really, Shimon was Torem from Reuven's produce. The case is, Reuven said, 'Whoever wants to Torem may do so.'

Answer #2: R. Avahu taught that if Shimon is Torem his produce to exempt Reuven's, Shimon has Tovas Hana'ah.

Bechoros 11a - Rav Shizbi: If Shimon redeemed Reuven's Peter Chamor, it is redeemed.

Rishonim

Rambam (Hilchos Terumos 4:2): Shimon cannot be Torem Reuven's produce without Reuven's permission. However, Shimon can be Torem his own produce to exempt Reuven's. The Tovas Hana'ah is Shimon's.

Question: The Gemara did not resolve whether or not it takes effect. Why do the Rambam (and Tur and Shulchan Aruch) say that it takes effect?

Answer #1 (Kesef Mishneh and Ri Korkus): After this question, the Gemara asked about who has Tovas Hana'ah. This implies that we know that Terumah takes effect.

Rebuttal #1 (Mishneh l'Melech): Even if Shimon cannot Torem Reuven's produce without permission, we need to ask about Tovas Hana'ah when he had permission!

Defense (Beis Yosef YD 331 DH u'Mah she'Chosav): If Shimon had permission he is like Reuven's Shali'ach, surely Tovas Hana'ah would be Reuven's! (Tosfos (Bava Kama 68b DH Hu) says similarly regarding Pidyon Peter Chamor - Mishneh l'Melech.)

Rebuttal #2 (Gra YD 331:73): The Ran (Nedarim 36b DH Ela a'Da'ata) explains that the one who asked whether or not Shimon can Torem Reuven's produce without permission knew that (if it works) the Tovas Hana'ah would be Shimon's. This shows that even though we conclude that Shimon would have Tovas Hana'ah, this does not imply that we are sure that it works!

Answer #2 (Ritva Kidushin 23b DH Ela): Our Gemara sought to resolve the question from Tana'im; it failed. Nevertheless, it is resolved from Rav Shizbi (Bechoros 11a), who taught that if Shimon redeemed Reuven's Peter Chamor, it is redeemed.

Rebuttal (Tosfos Bechoros 11a DH ha'Podeh): Even though Shimon can give his own money or Seh to redeem Reuven's Peter Chamor without Reuven's Da'as, this was not resolved regarding Terumah. Regarding Terumah it says "Gam Atem" to include a Shali'ach, but he must be like you, i.e. with your consent.

Defense (Mishneh l'Melech): We learn Shlichus from Terumah to the entire Torah! If permission was needed for Terumah, it would also be needed for Peter Chamor.

Ri Korkus - even though "Tevu'as Zar'echa v'Nosata" suggests that the owner of the produce gives (to whom he wants), "v'Nosata" actually refers to "Aser Ta'aser" (the one who was separated Ma'aser).

Rambam (Hilchos Nedarim 6:6): If a vow forbids Reuven to benefit from Shimon, Shimon may Torem Reuven's produce with Reuven's consent. E.g., Reuven said 'whoever wants to Torem may do so.' However, if Reuven asked Shimon to do so it is forbidden, for he benefits him by fulfilling his mission.

Lechem Mishneh: Even though the Gemara concluded that Shimon may Torem his own produce to exempt Reuven's, also this (it is not considered Hana'ah when Reuven said 'whoever wants') is true.

R. Avraham Min ha'Har (Nedarim 36b DH Lo): If a vow forbids Reuven to benefit from Shimon, Shimon may not Torem his produce to exempt Reuven's. Even though paying a debt is not called giving benefit (it merely prevents a loss), taking Terumah permits Reuven's produce, which was forbidden.

Poskim

Shulchan Aruch (YD 331:30): If Shimon was Torem Reuven's produce without permission it does not take effect. If he was Torem his own produce to exempt Reuven's it takes effect, and Shimon has Tovas Hana'ah.