mulberry hefker and jam
Question
In the yard of my apartment building there is a mulberry tree, next to the parking lot. Most of the residents aren't interested in picking the fruit and in regular years we do. Am I allowed to harvest the berries and prepare jam, just as I do during regular years and like I used to do in the United States, in my childhood?
Answer
Hefker for trees of shared ownership
A tree that is situated in an area of shared ownership belongs to all residents of the building. If the other residents are willing for others to pick the berries, you can do so just like during regular years.
However, shemitah produce is supposed to be rendered ownerless and not guarded. If we assume that the residents don't care if others come to harvest the berries (and assuming that berry pickers do not harm the tree, enter the area late at night, or do any other damage), and since the yard is not locked or fenced in, I recommend making it hefker in the name of all residents of the building before three friends (the halachic term for this is אוהבים). See here for the way to render a tree hefker before three friends. In this way you can perform the mitzvah of hefker while your neighbors will not complain that strangers are mulling around the yard. If there are lots of fruits, it is best to actively encourage these friends to come and harvest the fruit. Of course, make sure that fruit pickers avoid damaging the garden or disrupting the rest of the residents.
Preparing mulberry jam
Since cooking mulberries and turning it into jam is considered a conventional use of this fruit, it is not a problem to do so this shemitah as well, and prepare enough jam for an entire year.
While strawberry jam is much more widespread and conventional, I believe that mulberry jam is also conventional and certainly not unusual. As you noted, in your childhood in America you used to make mulberry jam from the fruit growing on your tree in your yard. Even if in Israel most people with mulberry trees in their yards do not make jam from the berries, in my humble opinion, if among those from North American backgrounds this is considered conventional, halachically it is still considered a conventional use for shemitah purposes. For more on this topic, see chapter 16 of The Consumer's Guide for Shemitah, nn. 2–4.
I have seen that mulberry liquor is also prepared and sold.
If the alternative to preparing mulberry jam is that no one will eat the berries and they will all go to waste, then it is all the more permissible to make jam, even if it is not considered conventional here in Israel (see ibid., n. 6).
It is possible to throw away regularly the small stems of the berries. They are not edible, thus do not have kedushat shevi'it.
Cleaning for insects
Note that mulberries (along with raspberries, blackberries, and other similar types of berries) are generally highly infested. Due to their size and structure it is virtually impossible to clean them completely of insects. Even when pulverizing them, whole bugs are often left intact. Therefore, in order to ensure that your do not eat insects along with your jam (several biblical prohibitions!), it is important to strain the jam through a fine mesh jelly strainer (at least 90mesh) after cooking it. This will give you a clear, kosher, and holy jam. Whatever fruit is left on the filter is still holy and should be stored for two days in a shemitah bin and then disposed.
Bi'ur
Note bi'ur time for mulberries is late this coming September. That means that you will need to remember to render the jam ownerless in front of three people. After leaving it out for a half-an-hour, you can claim the jam. For more on the laws of bi'ur, see The Practical Laws of Bi'ur from The Consumer's Guide to Shemitah, here.
See also an abridged version (from Shemitah on One Foot) here.
Bon appetite!