"A series from one to three items" - is it syntactically correct construction?

First, 'a series from one to three items' leaves an impression that the series somehow spans the space between one item and three items, rather than that it consists of at least one item, but no more than three items, which appears to have been intended. As Mr. Yargs has pointed out in a comment, an of is needed to convey that the series consist of these items: the formulation should thus be 'a series of from one to three items' or, better, 'a series of one to three items'.

Setting that aside, can one speak of a series that consists of only one item? The answer depends on one's audience. An audience trained in the sciences, engineering, or some related field, won't see anything strange about using the term series (or the related terms sequence and set) for something that, in fact, has only one member, as long as its nature allows for having more. But then, people with such training tend to use series with a very precise meaning that is not very useful for referring to one to three indistinguishable hyphens, as has been pointed out by FumbleFingers in a comment. An audience without such training is likely to find the idea of a one-member series (or set or sequence) confusing regardless of what it consists of.

The problem can be entirely avoided by simply saying that a connector consist of one to three hyphens.