Дал команду, получил такой вывод:
Check container passed.
Check sign passed.
Check verify signature on private key passed.
Check verify signature on public key passed.
Check import passed.
Keys in container:
exchange key
Extensions (maxLength: 1435):
ParamLen: 47
OID: 1.2.643.2.2.37.3.10
Critical: FALSE
Size: 19
Total: SYS: 0,010 sec USR: 0,120 sec UTC: 7,090 sec
[ErrorCode: 0x00000000]

Получается не экспортируемый, соответственно не перенести?

Точно, не весь вывод указал. Но раздела permision все равно нет:
CSP (Type:80) v4.0.9014 KC1 Release Ver:4.0.9842 OS:Linux CPU:AMD64 FastCode:READY:AVX.
AcquireContext: OK. HCRYPTPROV: 35276547
GetProvParam(PP_NAME): Crypto-Pro GOST R 34.10-2012 KC1 CSP
Container name: "ContainerName"
Signature key is not available.
Exchange key is available. HCRYPTKEY: 0x21d54b3
uec key is not available.

CSP algorithms info:
Type:Encrypt Name:'GOST 28147-89'(14) Long:'GOST 28147-89'(14)
DefaultLen:256 MinLen:256 MaxLen:256 Prot:0 Algid:00026142

Type:Hash Name:'GR 34.11-2012 256'(18) Long:'GOST R 34.11-2012 256'(22)
DefaultLen:256 MinLen:256 MaxLen:256 Prot:0 Algid:00032801

Type:Signature Name:'GR 34.10-2012 256'(18) Long:'GOST R 34.10-2012 256'(22)
DefaultLen:512 MinLen:512 MaxLen:512 Prot:0 Algid:00011849

Type:Exchange Name:'DH 34.10-2012 256'(18) Long:'GOST R 34.10-2012 256 DH'(25)
DefaultLen:512 MinLen:512 MaxLen:512 Prot:0 Algid:00043590

Type:Exchange Name:'DH 34.10-2012 256'(18) Long:'GOST R 34.10-2012 256 DH'(25)
DefaultLen:512 MinLen:512 MaxLen:512 Prot:0 Algid:00043591

Type:Hash Name:'HMAC GOST 28147-89'(19) Long:'HMAC GOST 28147-89'(19)
DefaultLen:32 MinLen:32 MaxLen:32 Prot:0 Algid:00032799

Status:
Provider handles used: 3
Provider handles max: 1048576
CPU Usage: 29 %
CPU Usage by CSP: 0 %

Virtual memory used: 3167672 KB
Virtual memory used by CSP: 146964 KB
Free virtual memory: 2723552 KB
Total virtual memory: 5891224 KB

Physical memory used: 1885316 KB
Physical memory used by CSP: 7424 KB
Free physical memory: 73752 KB
Total physical memory: 1959068 KB

Key pair info:
HCRYPTKEY: 0x21d54b3
AlgID: CALG_DH_GR3410_12_256_SF = 0x0000aa46 (00043590):
AlgClass: ALG_CLASS_KEY_EXCHANGE
AlgType: ALG_TYPE_DH
AlgSID: 70
KP_HASHOID:
1.2.643.7.1.1.2.2
KP_DHOID:
1.2.643.2.2.36.0
KP_SIGNATUREOID:
1.2.643.2.2.36.0
Permissions:
CRYPT_READ
CRYPT_WRITE
CRYPT_IMPORT_KEY
CRYPT_ARCHIVE
0x800
0x10000
0x100000
KP_CERTIFICATE:
Not set.

Container version: 2
Keys in container:
exchange key
Extensions (maxLength: 1435):
ParamLen: 47
OID: 1.2.643.2.2.37.3.10
Critical: FALSE
Size: 19

Точно, пропустил. Спасибо! Пошел генерить заново :)