This certainly is possible---but unless you define the "several ways" to verify that A has the funds, the solution must exclude this key component. Here is one possible solution:
Special Multisignature Bitcoin-Address
Create a 3-of-5 multisignature Bitcoin address to which A transfers the Bitcoin in question. A owns 3 of the 5 participating addresses, whilst B and C contribute one each. Next A prepares a partially signed transaction that is signed with only one of his keys.
To eventually access the funds, B and C must both sign this transaction (or ask A for further signing). But it does not tie up the funds in that A can still access the Bitcoin using only his own keys.
Note that this only protects A from either B or C unilaterally taking possession of the bitcoins involved, but it does not offer any reassurance to B or C that the bitcoins will remain available to them in the future. That may create a particularly perverse incentive for intermediary B and recipient C to conspire into splitting the pot among them rather than adhering to whatever B's responsibilities in this matter were supposed to be.