Question: rotation of Sun's core?

Someone who I don't consider a very credible source was trying to tell me
yesterday that there is a known theory that the Sun's core rotates at the
same speed as Earth's core... can anyone shed some light on this for me
please?

Advanced Google: "rotation" and "solar core" gets you 4190 hits,
including
[Only registered users see links. ]
where you can learn that the rate of rotation of the solar core varies
with time and with depth.

BTW, what you refer to is not called a 'theory' in empirical science,
but rather an 'hypothesis.'

It is accorded the status of a 'theory' when it is able to make
quantitative predictions regarding the outcomes of physical
measurements.

When, as in the case of this concept, it has been demonstrated by
physical measurements (helioseismology in this case) to be inconsistent
with the observable universe, it is reclassified as 'crap'.

You will see a lot of such around here, posted by people who either are
ignorant of the data, or choose to ignore the data.
Tom Davidson
Richmond, VA