I have read through the JAR-OPS 1.945, and mine might be out-of-date, but I can't find anything about the 15 day limit, and just to point it out: this paragraph is for conversion course. Not full typerating course. I checked it up with my authorities which confirms my understanding of it; There is no time limit between end of TR end commencement of linetraining. If it did, what about all of those funding their own TR without any job offer...?
But they told me that the basecheck/circuits is regarded as part of LST, in the sence that the mentioned time limit of 6 months from start of TR to LST is applicable-we need to have completed the circuits before the 6 months have elapsed.