Tosefta על ביכורים 1:8

Rabbi Yehuda says, until [he brings them] to the Be'er HaGolah (per Lieberman, an area on the perimeter of the Temple Courtyard), he remains obligated in the responsibility [of bringing first fruits]. From [the point that he brings the fruit to] the Be'er HaGolah, he is no longer obligated in the responsibility. Rabbi Shimon ben Yehuda says in the name of Rabbi Shimon, as for one who must replace [the first fruits if they were robbed or rotted (see Bikkurim 1:8)], he is not liable [to pay an extra] fifth in addition to [the replacement].