Once __ , he threw himself into his work and made every effort do it well.

答案不是having recoverd ，原因如下：
（如下从字典里搬来的）
1. 重新获得;重新找到
Jane recovered her lost wallet.
简寻回了丢失的钱包。
2. 恢复;使恢复原状
Jennie made a great effort to recover herself.
珍妮努力使自己镇定下来。
She has recovered her health.
她已恢复了健康。
3. 挽回,弥补
It's hard to recover lost time.
弥补失去的时间并不容易。
4. 【律】取得(损害赔偿);取得...的所有权
5. (填海)造(地),围垦[(+from)]
vi.
1. 恢复健康;恢复原状;恢复[(+from)]
It took a long time for him to recover from a bad cold.
他患重感冒,很长时间才康复。
I think she will recover.
我想她会痊愈的。

以上可以看出，recover oneself 是指某人身体恢复，
如果要说某人康复，可以用主动，亦可用被动。
主动表示方法：
He has recovered himself.
被动表示方法：
He has being recovered.
上句中，Once后面如果接的是个完整的句子，应该为：
Once he had been recovered ,....
省略掉之后是：Once having been recovered,.....

答案是B，Once (he) recovered (himself),...

RECOVER表示康复时是不及物动词

vt. 重新获得, 恢复, 复原, 拯救
vi. 痊愈, 复原, 胜诉
例句
He may possibly recover.
他或