I think this is possible in certain contexts (it is in Biblical Hebrew, for instance, with some differences). Where languages, such as Modern Hebrew in this particular case, tend to default to a subject-verb-argument(s)-complement(s) word-order (or clause-)pattern (sometimes called a subject-verb-object, or SVO, pattern, which might sometimes be slightly misleading), language speakers tend to default toward organizing information from information that they assume to be relatively old, already established, or readily accessible (to their audience/hearer[s]) to information that they assume to be relatively new, unestablished, or inaccessible (to their audience/hearer[s])—or, in other words, information that's being newly communicated. In linguistics, this is the principle of 'natural information flow'. (There are all sorts of reasons why the 'default' word-order can be broken, for example, in order to change or shift the center of focus/attention to a new topic/subject within a clause/sentence and a larger portion of a discourse, or in order to emphasize, highlight, or draw extra attention to some particularly relevant new information, to make it stand out even more, as particularly prominent/salient.)
As for the Duolingo's problem/example above, pronouns often refer to participants/entities/things that are already accessible to hearers, so that's likely part of the reason that מהם precedes עברית and gravitates toward the verb. (Prepositions and pronouns can also sometimes function like clitics that attach, for example, to the beginnings or endings of other words/phrases so that we pronounce them together, in which case they might receive relatively little or no stress when spoken. לך tends to gravitate toward יש in the stock phrase/expression "[יש לך [משהו" for probably these and similar reasons, which has come to form a highly conventional, established unit/construction in Hebrew.) Moreover, since, at the same time, עברית falls at the end of the clause/sentence after מהם, it's likely a relatively salient/prominent argument, placing the focus on 'what she is learning from them' rather than—or at least more than—'from who(m) she is learning Hebrew'. Notice in the audio for this example how the speaker pauses briefly following מהם and uses slightly higher intonation and stress on עברית.
Also, keep in mind that, generally speaking, the order in which information is introduced in a clause or sentence (through speaking or writing) is the same order in which the meaning/ideas/conceptions tend to be accessed or activated (most strongly) in the minds of hearers and readers, which can subtly shift how we think of, picture, or view a situation. Fluent speakers are so adept that they do much of this almost automatically without having to give it much conscious, long, effortful thought (especially in everyday conversation).
Sorry for the jargon and the overly detailed answer! 'Information structure' is an extremely complex subject in linguistics, not to mention Hebrew! It requires being selective and simplifying things somewhat. More examples would help, but I don't have the time at the moment.
Well, that was just amazing!! Might I add 2 small, not so nearly technically eloquent points: As English (or any native language) speakers we are most comfortable in the common word order of our mother tongue. Sometimes it works out, and sometime not. It took me forever to be comfortable with placing the time element immediately after the subject in Chinese--It's not acceptable elsewhere. For example She is not home today--is properly: She today is not at home. or I did it yesterday is properly: I yesterday did it. This is why, when non English speakers translate their language directly it is sometimes odd, or even comical, though usually understandable. For the most part Hebrew as a European thought/communication construct dressed up as a Semitic language follows SVO, as above, but not always. Oh, don't beat me up about the European thing--I borrowed the idea from Rutie Adler's grammar book זה לו נורה (It's Not So Bad).
Additional contextual factors might justify the word order that Corinna originally asked about. For instance, what if the speaker assumed that what the woman was learning (i.e., Hebrew) was already relatively accessible and/or established in the communicative (or discourse) context and could thus be referred to with a pronoun? He might then say ”היא לומדת אותה מהם”.
Or, what if, in addition to this, it was not known who was instructing her and so the speaker used proper names? He might say ”היא לומדת אותה מאברהם ושרה”.