AMC1 FCL.050 Recording of flight time
GENERAL
(a) The record of the flights flown should contain at least the following information:
(4) details on pilot function, namely PIC, including solo, SPIC and PICUS time, co-pilot, dual, FI or FE;
It is a requirement to record if you acted as an Instructor but not what instruction was given, nor to whom.
Of course these details can be recorded if wished and may be useful in the future: ie Wanting to work for a new school and showing the breadth of personal instructional experience.
How do you prove its flight instruction if it does not contain relevant details including the studen's name?
(a) A student having lost their records: Other means of ascertaining this.
(b) An Instructor wishing to prove their experience (eg as one of the Revalidation requirements): Taken on trust as not really possible to prove (just like an SEP Holder wanting to Revalidate 'By Experience').