What actually gets lost
A handover document lists the account value, the contacts, the open opportunities and the renewal date. It never contains the reason the client will not take a call before eleven, the previous supplier they left badly, or the fact that the person with the budget is not the person on the calls.
That knowledge is not in a system anywhere. It is in one person's head, and it leaves when they do.
Write the handover from the conversations, not from memory
If your calls are recorded, the handover writes itself from the record rather than from what the departing person remembers on their last week — which is a poor sample, because it is weighted entirely toward the last month.
Search the account for the words “concerned”, “worried”, “budget” and “we tried”. Almost everything that matters is in the sentences around those.
Three things the next person needs first
How this client likes to be dealt with. Formal or not, email or call, whether they want detail or a summary. Getting this wrong in the first interaction costs months.
What they have already been promised. Anything committed on a call and not written down is still a commitment, and the fastest way to lose a handed-over account is to fail one nobody recorded.
What they were unhappy about, and whether it was resolved. Every account has one, and the new person finding out about it from the client is the worst version of that conversation.
Introduce, do not transfer
A handover email is a transfer. A joint call where the departing person says what they think matters, in front of the client, is an introduction — and it lets the client correct anything wrong before it becomes the new person's understanding.
It also, usefully, produces a recording that contains the entire handover.
The obvious caveat
If your calls are not recorded, none of this is available and the honest answer is that a good handover then takes several hours of conversation with the departing person, booked before their notice period gets busy.
That is worth doing regardless. A tool is not a substitute for it.