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There is an obligation to recite each year during the month of Nissan "Birkat Ha'ilanot," a Beracha over the sighting of a budding tree.
The question arose regarding the case of a community that had the practice to recite Birkat Ha'ilanot together over a tree in a certain person's yard each year. Eventually, the resident of this home passed on, and some members of the community sought to choose a different tree for the annual recitation of Birkat Ha'ilanot.
The Halacha regarding such a case relates to a ruling in the Shulhan Aruch (Orah Haim 366:3) relevant to the law of Eruv. Whenever residents sharing a courtyard join together to make an Eruv in order to allow them to carry on Shabbat in the courtyard, they must purchase some bread or Masa and keep it in one of the residents' homes. The Shulhan Aruch ruled that if the Masa had been kept in certain resident's home for an extended period of time, they should not unnecessarily move it to a different resident's home. Doing so might give rise to some suspicion regarding the first resident, as people may think that he is no longer observant or is otherwise unqualified to keep the Eruv in his home. The Mishna Berura (commentary to the Shulhan Aruch by Rabbi Yisrael Kagan, 1839-1933) adds (366:26) that this applies even after the first resident's passing. The bread or Masa should remain with the inheritor of the home, unless some compelling reason dictates doing otherwise.
Rav Pinhas Zevihi (contemporary), in his work Birkat Yosef (p. 145; listen to audio recording for precise citation), applies this concept to Birkat Ha'ilanot, as well. Even though discontinuing the recitation of Birkat Ha'ilanot over a person's tree does not necessarily reflect anything negative about him, it is still improper and insensitive for a community to suddenly change to a different tree. Assuming the tree remains fully accessible, a community that had been accustomed to reciting the Beracha over a certain person's tree should continue to do so, even after that individual's death, not to mention during his lifetime.
Summary: If a community had been accustomed to reciting Birkat Ha'ilanot each year over a certain person's tree, it is proper for them to continue this practice, and they should not change to a different tree unnecessarily even after that individual's passing.