If U-238 captures a neutron, Plutonium with mass 239 is created. The atomic number then becomes 94. So two protons have been added to the nucleus. Where do they come from then?

Answer

In nuclear reactions, sometimes a neutron is converted into a proton + an electron. This process is a form of beta decay, more specifically “beta-min decay”. The reverse (“beta-plus decay”) is also possible under certain circumstances: a proton emits a positron and transforms into a neutron. All this always happens according to the (conservation) laws of quantum mechanics, in particular the conservation of charge.
The number of neutrons in a heavy atomic nucleus can take on different values, these are called isotopes. Iron, for example, always has 26 protons and usually 30 neutrons, but there are also iron nuclei with a few neutrons more or less. If you keep adding neutrons to such a nucleus, the nucleus will become unstable at a certain point, and a neutron will be converted into a proton+electron. That electron is necessary because otherwise the total charge in the conversion would not be preserved. For example, iron with 32 neutrons is still stable, but with 33 it is no longer stable. Such a nucleus will spontaneously convert into a stable cobalt nucleus, the next element in Mendeleev’s table.

Uranium(238) + neutron initially gives Uranium(239) that spontaneously decays into Neptunium(239) + electron + energy.
This Neptunium(239) then decays in the same way into Plutonium(239) + electron + energy
This plutonium itself is not stable either, but its half-life is very long.

U(238) + n U(239)
U(239) ⇒ Np(239) + e^– (half-life = 23.5 days)
Np(239) ⇒ Pu(239) + e^– (half-life = 2.36 days)

Globally, two neutrons have been converted into two protons, and two electrons with a negative charge start walking, so that the total charge accounting remains the same.

And then comes:
Pu(239) ⇒ U(235) + He(4) (half-life = 24000 years)