Short Answer: NOT the "Living" individuals/persons.
We do not have our OWN "Tree" in "Family Tree" of 'FamilySearch'.
We ONLY have "Branches" (ie. Ancestral" lines), that are interconnected, in this SINGLE "One" World "Tree", for all of us, that is "Family Tree" of 'FamilySearch'.
That said ...
Provided, of course, that other family members and extended relatives have their OWN 'FamilySearch' Account, just like you ...
As you; and, other family members and extended relatives, are "Living" Users/Patrons ...
You; and, other family members and extended relatives, WILL have to "Added" SEPERATELY (and, 'Yes' as DUPLICATES) the "Living" individuals/persons that connect/link you together in your respective 'FamilySearch' Accounts ...
Basically, you; and, other family members and extended relatives, have to "Build" a "Bridge" of the "Living" individuals/persons that connect/link you together in your respective 'FamilySearch' Accounts ...
Once, you have built that bridge; then, when you come to your FIRST Common "Deceased" Ancestor your "Ancestral" lines will connect/link together into one ...
Let me explain ...
[ Please bear with me ... I am very verbose ... that is my 'Style' ... ]
"Family Tree" of 'FamilySearch' is NOT like 'On-Line' "Websites" (eg. "Ancestry_com"; or "MyHeritage_com"; or, the like); and/or, 'standalone' personal (computer) programmes (eg, the OLD, now no longer supported, "PAF"; or, "Ancestral Quest"; or, the like).
We DO NOT have "Private"/"Personal" 'Trees' in "Family Tree" of 'FamilySearch' like other 'On-Line' "Websites"; and/or, 'standalone' personal (computer) programmes.
We do not even, own; or, manage; and, are NOT even responsible for, the "Deceased" individuals/persons in "Family Tree" of 'FamilySearch'.
"Family Tree" of 'FamilySearch' is built on a "Open Edit" Platform - hence, why any registered User/Patron can "Edit" (ie. Add, Delete; and/or, Change) ANY "Deceased" individual/person in "Family Tree" of 'FamilySearch'.
You can certainly "Merge"/"Combine" any "Deceased" individual/person in "Family Tree" of 'FamilySearch' with another "Deceased" individual/person in "Family Tree" of 'FamilySearch', regardless of who the User/Patron was that initially created those "Deceased" individuals/persons; as, they DO NOT reside with the User/Patron who initially created them - they are "Public".
If fact, you can ONLY see "Deceased" individuals/persons in "Family Tree" of 'FamilySearch'; except, with this 'rider', that you can ALSO only see "Living" individual/person in "Family Tree" of 'FamilySearch' that YOU created; as, they reside in your "Private Spaces".
No other User/Patron can see ANY "Living" individuals/persons that were created by another User/Patron; as, they ONLY reside in the "Private Spaces" of the User/Patron who created them.
We CANNOT even see the ACTUAL Record in "Family Tree" of 'FamilySearch' of our IMMEDIATE Family (eg. Spouse; Children; Parents; Siblings; ETC; Etc; etc) if they are "Living"; and, they have their own 'FamilySearch' Account.
Of course, you can create your "Living" Family members; and, record them in "Family Tree" of 'FamilySearch'; but, they will ONLY be seen by you:
▬ You cannot "Share" them with any other User/Patron.
▬ You cannot "Merge"/'Combine" them with any other "Living" individual/person residing in the "Private Spaces" of another User//Patron.
There is CURRENTLY no mechanism in "Family Tree" of 'FamilySearch' for Users/Patrons, to "Share"; or, "give permission" to "Share", the "Living" individuals/persons in their own "Private Spaces" with/between other/another User(s)/Patron(s).
There are a myriad of "Privacy" Laws within the many various Countries and Unions throughout the World - it is a nightmare to negotiate.
"Family Tree" of 'FamilySearch' is used in many Countries and Unions throughout the World; and, as such, must adhere to the myriad of "Privacy" Laws throughout the World.
Hence, "Privacy" is one of the reasons that we cannot "Share" the "Living" individuals/persons in our own "Private Spaces" - it is NOT the ONLY reason; but, certainly has a bearing on the matter.
Another factor is that such would have to be 'Coded'/'Programmed' into the Programme that is "Family Tree" of 'FamilySearch'.
'Yes', these "Living" individuals/person in "Family Tree" of 'FamilySearch' WILL, in fact, in many (most) cases will be "Duplicated" - unfortunately a necessary situation that currently cannot be avoided.
I know that there are "Duplicates" of the "Living" ME - at least, one for my Wife and each of our Children, not to mention my other ("Living") extended Family members.
Here are some "Knowledge Articles" in 'FamilySearch' in regard to "Private Spaces" and "Living" individuals/persons:
What is a private space in Family Tree?
Who can see my living relatives in Family Tree?
Here is a good place to start, with how things work in "Family Tree" of 'FamilySearch' (and, other programmes as well):
Introducing The Family History Guide
The Family History Guide
I hope this helps.
Since all deceased individuals in the FSFT are already accessible to both you and your wife (as well as every other person with an account in FS), you must be talking about only the live person records in the private space of your account.
If you have a LOT of living person data in your private space, using a free copy of Ancestral Quest, you could very quickly download all of those individuals to your PC or Mac. Your wife could then go into that AQ database, log into her account, and then upload those AQ records to her private space in her account. Other applications could probably be used for this too such as RootsMagic, but I'm not familiar with it.
For someone familiar with this tool, the whole process for a dozen names could be done in about 20-30 minutes (including all of the sources). However, if there are not a lot of names and you are not familiar with AQ, it would likely be just as fast to bring up two windows, one logged into your account and one logged into hers, and just manually copy paste everything across.
Note that even though FS can sync with some other services such as Ancestry.com or MyHeritage.com, the last time I looked they were blocking the transfer of living individuals between those services.