Is it possible to write Hebrew in Arabic script and vice versa?

Hebrew in Arabic—in principle, yes: Arabic has a direct equivalent of every Hebrew letter, plus six more. However, there are four caveats to this:

1. The Hebrew gimmel, by default, is a hard g sound—whereas in Arabic, the equivalent letter (ج – jim) is like a soft g (/dʒ/), like the English j. However, it could be decided that it is pronounced like a hard g, as in Egyptian Arabic.
2. The Hebrew vav sounds like /v/, but its equivalent Arabic letter, waw (و) is pronounced like the English w. However, it could be decided that it is pronounced /v/, since Hebrew has no /w/ sound.
3. The Arabic script has no hard /p/ letter—however, the Persian script (which is a near-identical derivative) does (پ)—so that could be used.
4. The Hebrew tzadi is pronounced /ts/, but its Arabic equivalent, ṣād (ص) sounds like /s/—so one would have to decide that it is pronounced /ts/.

Arabic in Hebrew—at a pinch, but with difficulty, since Arabic has letters and sounds, such as tha (ث), dhal (ذ), ḍād (ض), ghayn (غ), ẓā’(ظ), that have no Hebrew equivalent (in sound or in letter), so would have to be represented with the closest Hebrew equivalent with some kind of added diacritic.

(Originally written in reply to a question at Quora.com).