According to the rules on Verditius magus, the way you graduate is that you provide an apprenticeship piece. If it works, you are in. The parens gets the item. Fair enough. But would there not be a lab text for that item as well? Does the Verditius have a lab text for some item that he could invent in a season for free? Or should a Verditius use some of his spell levels at the start to buy levels in an effect that he invented? Or should the whole thing be ignored?
No clear cut answer here. As written in the rulebook (I do not have the HOH:MC book), a magus gets no equipment at all when he starts play. That means that ptobably the lab text is kept buy the parens as well.
However, you can say otherwise and yes, the veritius has the lab text. Up to you, really 
I would allow it
Cheers,
Xavi
I'd allow it too,
However, bear in mind that the "Masterpiece" should be something the Master would approve of (otherwise they would not have ended their apprenticeship) - so it may be worth discussing with the player the sorts of things he/she is able to produce that might meet with their approval,
That said, it may be the case that the Master retains the lab text for their own use (the lab texts have some value too) - of course, it may be acceptable for the former apprentice to copy it. Perhaps it should also depend upon their relationship with their parens (tormenting master!)?
Would the lab text be useful to the parens? My understanding is that unless rewritten, lab texts are written in a code that is peculiar to the magus. I could understand that normally the parens should be able to read the code of his apprentice. In my case, my character was adopted by another Verditius just a few years before graduation because his previous master had gone into Final Twilight .
Then, the parens might well have a superior lab text for the item that I would be creating. For instance, coming out of apprenticeship, with all the bonuses I can find, I can generate a Lab total of 36 to create an effect that casts a The Call to Slumber effect (Lab Total: Re:+5 Me:+5 Intelligence:+2 Magic Theory: +5+1 for enchanting items Aura:+3 Inventive Genius:+3 Craft: 4 (Iron Wand) Shape and Material Bonus: +4 from wand (affect something from a distance) Philosophae:+2 (bonus from shape and material +Philosophae limited by Magic Theory) Similar Spell: 2 For a Lab Total of 36.) So base effect is 4, +3 magnitudes for Sight, and +3 to level for 6 times per day. A useful item that graduates me from my apprenticeship, but if my parens probably can generate a Lab total of 40, with his scores, he can then make three or four wands per season with 24 uses per day for exactly the same vis per wand. If so, my lab text is not going to cut it.
Fair point - I guess you may have been expected to "write up" the lab text for your parens, but that does leave the original free,
The parens may well have a lab text - but then again they may not, I would imagine that parens might be slightly more easily appeased if the item is actually useful to them, or at least new (rather than "oh, another ..., put it on the pile then").