This is related to a previous question of mine: Rate of linguistic change among geographically separated descendants of a common language
If you had 4 groups of humans with the same language and writing system, and these four groups were separated for approximately 15,000 years, how much would the writing system plausibly change in that period?
I think this question is worth asking separately as writing systems tend to change slower than spoken languages, and are often flexible enough to accommodate pretty significant phonological changes over time. Wholesale shifts to a brand-new writing system are exceedingly rare (Hangul script for Korean may be the only example). Beyond minor refinements in shape or simplifications, the major changes (such as adding or losing letters) seem to happen when one language adopts another language's writing system (see the adaptations made to the original Latin alphabet by other European languages).
In this situation however, each culture starts with the same language and writing system, and any developments are entirely internal. To rephrase the earlier question: even if over the period of separation the 4 cultures' spoken languages changed so much as to be completely unrecognizable phonologically or even morphologically, would it be plausible that their orthography would be broadly recognizable as having a common ancestor?