...But by the virtue of mastodon being only one open source platform that works on the overall federated universe and employs the OStatus protocol, there isn't anything stopping such a service as you described from being built...well, except for twitter eventually deciding to block access to their platform...but i'd guess that would turn the federated universe into a sort of social network martyr.
Anyway, sorry i digress...To answer your question a bit more concretely, there are options for what you asked about:
...But by the virtue of mastodon being only one open source platform that works on the overall federated universe and employs the OStatus protocol, there isn't anything stopping such a service as you described from being built...well, except for twitter eventually deciding to block access to their platform...but i'd guess that would turn the federated universe into a sort of social network martyr.
Anyway, sorry i digress...To answer your question a bit more concretely, there are options for what you asked about:
* https://github.com/halcy/MastodonToTwitter
* https://medium.com/@pimterry/sync-your-mastodon-back-to-twit...
I'm sure there are more options; try googling. Cheers!