Thank you all.
Bernie:
Indeed I was told that I may upgrade a B class. I bought the ticket because it was there for purchase. There was no other price option to select from on coach. I was unable to tell before the purchase what fare class it is, although I rtied to understand the fare rules... My ignorance.
Bernie:
If I understand you correctly, then, its UA that is unwilling to enable this upgrade request of an H to business on LH?