[burnished]

I'm not an expert so a pinch of salt is warranted but:

When you give some one money with legally recognized conditions then the organization has to honor those conditions. e.g donate money to a charity and tell them that it is to be used purchasing pens then that is all that money can be used for.

So if I understand correctly the 'scheme' here is that Lab A applies for and receives a grant that has stipulation X. As part of this process a portion of that grant goes to the hosting university without that stipulation. The university is free to spend that money however they wish, including providing some funds to Lab A for things that they really need but were not provided for under the grant.