Updating the covenant on a property

[thekingisdead]

Wasn't sure whether to post this in the finance section or "homes, gardens & DIY", but think its more appropriate here.
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I have a property that currently shares a septic tank with an adjacent property. The costs of maintaining the tank are split 2/3rd / 1/3rd between the two houses.

Next door have contacted me as they would like to install their own tank (having building work done anyway), and therefore require the covenant updating (I have no objections to the work / update)

Is it as simple as instructing my solicitor to update the covenant on my property? (And next door on theirs)
Or would it be simpler to instruct one solicitor to update both (potential conflict of interest?).
Presumably at some point each party must be able to review the covenant of the other property to ensure everything correlates?

Their are no issues with the relationship with the neighbours, but obviously with property matters such as these it's best to be done formally / correctly.
Cheers

[softtop]

why incur costs? Why not wait until you move as I am sure you are not going to be invoicing them for emptying your tank?

[thekingisdead]

The property is up for sale anyway - I am keen to get the covenant update prior to any sale - to avoid complications / slowing down the sales process.
We've already agreed to empty the tank on / around the date of next door switching to their own septic tank.