Move asset to LLC before selling? Will it really matter?

[Gail W.]

Need some help figuring this out...  

The Mr earns @ $100k on his W2 job. He will retire from that this mid December. We live in California, but will move permanently to AZ in December.

We own 3 rental properties in AZ; one being a park model that is a STR that we have had for 14 months.

We created an AZ LLC. We were about to put the Park Model in to the LLC.

Current vacation renters just offered to buy the Park Model for $350k. We purchased the Park Model for $162k, and can claim around $30k cap exp for rehab, so tax basis of about $192k. 

Should we hurry up and put the park model into the LLC before the sale? If we are still living in CA, but the LLC is in AZ, will it help/matter?

OR- we can WAIT and sell it to them in January, AFTER we've officially moved to AZ. They are fine waiting, but I feel like a bird in the hand is apt to fly away when it sees something better... ;)

TIA!