RE: how would i recognize the construction disbursement for the improvements for the property

Who paid for the construction disbursement?  (I interpreted it was for the improvements of the replacement (purchased) property.)  

When was the improvements done?    

"The transfer of relinquished property is not within the provisions of Section 1031(a) if the relinquished property is transferred in exchange for services. Thus any additional production occurring with respect to the replacement property after the property is received by the taxpayer will not be treated as the receipt of property of a like kind." (Reg § 1.1031(k)-1(e)(4)).

The above exchange regulations became effective in 1991. 

In 2001, the IRS issued Rev. Proc. 2000-37, which in part established the idea of a Qualified Exchange Accommodation Titleholder (QEAT), an entity that can be used to work around the issue of improvements not being like-kind to the taxpayer's old property.  

Did your client use a QEAT?  If not, how was the improvement paid?  How much?

The sale transaction has to be reported in 2022 with F8824.  The replacement was in 2023.  What were you getting at king when you asked  "has anyone had a 1031 exchange transaction where the property is sold in one year and replacement property is purchased following year? 

Isn't it quite common?  If a property was relinquished in the last quarter (and at times in the third quarter), the replacement would likely fall in the next year, so long as the 180-day rule is satisfied.