Step 1: Recall the anatomy of the digital flexor sheaths - the thumb sheath is continuous with the radial bursa and the little finger sheath with the ulnar bursa.
Step 2: A frequent anatomical connection links these two bursae at the level of the wrist through the space of Parona, allowing infection to pass between the thumb and little finger.
Step 3: Consequently, suppurative tenosynovitis starting in the little finger can extend along the ulnar bursa, cross to the radial bursa, and reach the thumb, creating the classic horseshoe abscess - confirming statement b.
Step 4: The remaining choices fail: the affected finger lies in slight flexion not extension, spread is to the thumb rather than the index, and the condition needs urgent surgical decompression plus antibiotics rather than conservative care.
\[\boxed{\text{Little finger tenosynovitis spreads to the thumb}}\]