Q. I would like to know the rav’s opinion, if a person can daven Mincha erev Shabbos in such a way that by the time he finishes, it will already be after shkia?
How would one fulfill the mitzvah of tosefes shabbos, which requires a verbal statement of accepting Shabbos at least 2 minutes before shkia?

A. Shulchan Aruch (O.H. 261: 4) rules that after answering borchu on erev Shabbos one already accepts Shabbos on himself even if is still clearly daytime and is prohibited in performing any of the melochos.. Shaarei Teshuva (ibid. 1) quoting Dagul Mervava presents two degrees of acceptance of tosefes Shabbos. One is limited to the taking on the prohibitions of doing melochos. The other is receiving fully the holiness of Shabbos, usually accepted when answering borchu or by reciting the tefilos of Shabbos (see Mishna Berura ibid.)
In the case you presented, Horav Shlomo Miller Shlit”a advises to accept tosefes Shabbos before Tefilas Mincha, only in regards to the prohibition of melochos, thus permitting still the reciting of Mincha. Immediately after ending the amida, although it is already after the beginning of the shkia, he should receive the tosefes of complete kedushas Shabbos.
Undoubtedly it is better to be mekabel the full Kedushas Shabbos properly before sunset. (Whether kabolas tosefes Shabbos requires a verbal statement or after the fact one complies with thought only, see Mishna Berura 553: 3)

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”